{"id":54335,"date":"2024-12-10T21:05:31","date_gmt":"2024-12-10T13:05:31","guid":{"rendered":"https:\/\/swarma.org\/?p=54335"},"modified":"2024-12-10T21:05:31","modified_gmt":"2024-12-10T13:05:31","slug":"%e4%bb%8e%e5%ae%8f%e8%a7%82%e5%88%b0%e5%be%ae%e8%a7%82%ef%bc%8c%e7%83%ad%e5%8a%9b%e5%ad%a6%e5%ae%9a%e5%be%8b%e4%bb%8d%e7%84%b6%e6%88%90%e7%ab%8b%e5%90%97%ef%bc%9f%e4%bb%8b%e8%a7%82%e7%bb%9f%e8%ae%a1","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=54335","title":{"rendered":"\u4ece\u5b8f\u89c2\u5230\u5fae\u89c2\uff0c\u70ed\u529b\u5b66\u5b9a\u5f8b\u4ecd\u7136\u6210\u7acb\u5417\uff1f\u4ecb\u89c2\u7edf\u8ba1\u70ed\u529b\u5b66\u7406\u8bba\u4e0e\u5b9e\u9a8c"},"content":{"rendered":"
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\u5bf9\u4e8e\u5c0f\u7cfb\u7edf\uff0c\u6211\u4eec\u7528\u7c92\u5b50\u6570\u548c\u8fc7\u7a0b\u65f6\u95f4\u4e24\u4e2a\u5c3a\u5ea6\u523b\u753b\u5176\u4ecb\u89c2\u7279\u6027\u3002\u4e00\u65b9\u9762\uff0c\u7814\u7a76\u5bf9\u8c61\u4ece\u5b8f\u89c2\u5230\u4ecb\u89c2\u548c\u5fae\u89c2\uff0c\u4f34\u968f\u7740\u6240\u7814\u7a76\u7684\u7269\u7406\u7cfb\u7edf\u7684\u7c92\u5b50\u6570\u6216\u5c3a\u5bf8\u53d8\u5c0f\uff0c\u70ed\u6da8\u843d\u548c\u91cf\u5b50\u6da8\u843d\u53d8\u5f97\u81f3\u5173\u91cd\u8981\uff0c\u8fd9\u5bfc\u81f4\u4e86\u5982\u5c0f\u7cfb\u7edf\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u6216\u8005\u7eb3\u7c73\u70ed\u529b\u5b66\u7b49\u65b0\u5174\u5b66\u79d1\u65b9\u5411\u7684\u4ea7\u751f\uff0c\u7279\u522b\u662f\u5c0f\u7cfb\u7edf\u4e2d\u91cf\u5b50\u76f8\u5e72\u6027\u548c\u70ed\u5e93-\u7cfb\u7edf\u91cf\u5b50\u7ea0\u7f20\u63a8\u52a8\u4e86\u5173\u4e8e\u7edf\u8ba1\u7269\u7406\u57fa\u7840\u7406\u8bba\u7684\u524d\u6cbf\u7814\u7a76\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u6240\u7814\u7a76\u7684\u7269\u7406\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u8fc7\u7a0b\u65f6\u95f4\u5c3a\u5ea6\u53d8\u77ed\uff0c\u4f53\u7cfb\u504f\u79bb\u5e73\u8861\u6001\uff0c\u8fd9\u50ac\u751f\u51fa\u4e86\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7b49\u7814\u7a76\u65b9\u5411\u3002\u5176\u4e2d\uff0c\u52a8\u529b\u5b66\u63a7\u5236\u5bf9\u70ed\u529b\u5b66\u8fc7\u7a0b\u5f71\u54cd\u4e5f\u5df2\u6210\u4e3a\u8fd1\u4e9b\u5e74\u7684\u70ed\u70b9\u7814\u7a76\u65b9\u5411\u3002\u56fe1\u603b\u7ed3\u4e86\u7edf\u8ba1\u70ed\u529b\u5b66\u5411\u4ecb\u89c2\u5c0f\u7cfb\u7edf\u53d1\u5c55\u7684\u8fd9\u4e00\u65b0\u8d8b\u52bf\u548c\u524d\u6cbf\u65b9\u5411\u3002<\/span><\/p>\n


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\u56fe1 \u7edf\u8ba1\u70ed\u529b\u5b66\u53d1\u5c55\u201c\u65b0\u76f8\u56fe\u201d<\/span><\/section>\n<\/section>\n
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\u672c\u7efc\u8ff0\u662f\u5728\u7b14\u8005\u53ca\u5408\u4f5c\u8005\u4eec\u591a\u5e74\u5728\u4ecb\u89c2\u7edf\u8ba1\u70ed\u529b\u5b66\u9886\u57df\u7684\u7814\u7a76\u57fa\u7840\u4e0a\u7684\u603b\u7ed3\uff0c\u540c\u65f6\u4e5f\u53cd\u6620\u4e86\u56fd\u9645\u4e0a\u70ed\u529b\u5b66\u53d1\u5c55\u7684\u8d8b\u52bf\uff1a\u5728\u7a7a\u95f4\u5c3a\u5ea6\u4e0a\u4ece\u5b8f\u89c2\u5c3a\u5ea6\u8d70\u5411\u4ecb\u89c2\u5fae\u89c2\u91cf\u5b50\u7684\u5c3a\u5ea6\uff1b\u5728\u65f6\u95f4\u5c3a\u5ea6\u4e0a\u4ece\u5e73\u8861\u6001\u8d70\u5411\u6709\u9650\u65f6\u95f4\u7684\u975e\u5e73\u8861\u8fc7\u7a0b<\/strong>\u3002\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u53d7\u81ea\u8eab\u5b66\u8bc6\u7684\u5c40\u9650\u548c\u504f\u597d\u7684\u5f71\u54cd\uff0c\u672c\u6587\u5e76\u672a\u8bd5\u56fe\u3001\u4e5f\u4e0d\u53ef\u80fd\u5bf9\u6574\u4e2a\u9886\u57df\u8fdb\u884c\u5168\u9762\u7684\u3001\u6216\u8005\u5305\u7f57\u4e07\u8c61\u7684\u4ecb\u7ecd\uff0c\u53ea\u9009\u62e9\u4e86\u7b14\u8005\u6bd4\u8f83\u719f\u6089\u7684\u65b9\u9762\u8fdb\u884c\u9610\u8ff0\u3002\u5e0c\u671b\u80fd\u4e3a\u76f8\u5173\u7814\u7a76\u8005\u63d0\u4f9b\u4e00\u4e9b\u6709\u4ef7\u503c\u7684\u53c2\u8003\u548c\u501f\u9274\u3002<\/span><\/section>\n<\/section>\n

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2. \u91cf\u5b50\u70ed\u673a\u4e0e Maxwell \u5996<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u8fd120\u5e74\u6765\uff0c\u53d7\u5230\u91cf\u5b50\u4fe1\u606f\u53d1\u5c55\u7684\u5e26\u52a8\u4ee5\u53ca\u5b9e\u9a8c\u6280\u672f\u8fdb\u6b65\u7684\u5f71\u54cd\uff0c\u91cf\u5b50\u529b\u5b66\u548c\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u4e00\u4e9b\u57fa\u672c\u95ee\u9898\u91cd\u65b0\u53d7\u5230\u7269\u7406\u5b66\u5bb6\u7684\u5173\u6ce8\u3002\u91cf\u5b50\u70ed\u673a<\/span> (\u89c1\u56fe2) <\/span>\u4e3a\u7814\u7a76\u8fd9\u4e9b\u95ee\u9898\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f88\u597d\u7684\u5e73\u53f0\u3002\u987e\u540d\u601d\u4e49\uff0c\u91cf\u5b50\u70ed\u673a<\/strong>[1-3]\u662f\u4ee5\u201c\u91cf\u5b50\u7269\u8d28\u201d\u4e3a\u5de5\u4f5c\u7269\u8d28\u5e76\u4e14\u628a\u5438\u70ed\u8f6c\u5316\u4e3a\u5bf9\u5916\u505a\u529f\u7684\u673a\u5668<\/strong>\u3002\u7531\u4e8e\u5de5\u4f5c\u7269\u8d28\u7684\u91cf\u5b50\u5c5e\u6027\uff0c\u91cf\u5b50\u70ed\u673a\u5177\u6709\u5f88\u591a\u4e0d\u540c\u4e8e\u7ecf\u5178\u70ed\u673a\u7684\u975e\u51e1\u7279\u8d28\u3002\u91cf\u5b50\u70ed\u673a\u5de5\u4f5c\u7269\u8d28\u7684\u91cf\u5b50\u6027\u6210\u4e3a\u4e00\u4e2a\u5907\u53d7\u5173\u6ce8\u7684\u65b0\u7814\u7a76\u70ed\u70b9[4]\u3002\u4eba\u4eec\u8bd5\u56fe\u901a\u8fc7\u5b9e\u9a8c\u53d1\u73b0\u4e00\u4e9b\u6709\u522b\u4e8e\u4f20\u7edf\u70ed\u529b\u5b66\u7406\u8bba\u7684\u65b0\u73b0\u8c61\u548c\u65b0\u6548\u5e94\u3002\u5728\u7406\u8bba\u7814\u7a76\u65b9\u9762\uff0c\u4e00\u4e9b\u8d85\u8d8a\u4eba\u4eec\u4f20\u7edf\u89c2\u5ff5\u7684\u65b0\u5947\u7ed3\u8bba\u9646\u7eed\u88ab\u53d1\u73b0\u3002\u6bd4\u5982\uff0c\u5728\u4e00\u5b9a\u6761\u4ef6\u4e0b\uff0c\u91cf\u5b50\u70ed\u673a\u5728\u6bcf\u4e2a\u5faa\u73af\u8fc7\u7a0b\u4e2d\u7684\u5bf9\u5916\u505a\u529f\u91cf\u53ef\u4ee5\u8d85\u8fc7\u5bf9\u5e94\u7684\u7ecf\u5178\u70ed\u673a<\/strong>[5,6]\uff0c\u800c\u4e14\u91cf\u5b50\u70ed\u673a\u7684\u6548\u7387\u4f3c\u4e4e\u53ef\u4ee5\u8d85\u8d8a\u7ecf\u5178\u70ed\u673a\u7684\u6548\u7387\u4e0a\u9650\u2014\u2014\u7ecf\u5178Carnot\u70ed\u673a\u7684\u6548\u7387<\/strong>[7]\u3002\u91cf\u5b50\u70ed\u673a\u4e0d\u4ec5\u6709\u52a9\u4e8e\u7814\u7a76\u91cf\u5b50\u529b\u5b66\u548c\u70ed\u529b\u5b66\u7684\u5173\u7cfb\uff0c\u8fd8\u6709\u52a9\u4e8e\u7406\u89e3\u91cf\u5b50\u6d4b\u91cf\u548c\u91cf\u5b50\u9000\u76f8\u5e72\u95ee\u9898\u3002\u6b64\u5916\uff0c\u5b83\u8fd8\u80fd\u5f88\u597d\u5730\u4f53\u73b0\u91cf\u5b50\u548c\u7ecf\u5178\u70ed\u529b\u5b66\u7cfb\u7edf\u7684\u5dee\u5f02\uff0c\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u70ed\u529b\u5b66\u8fc7\u7a0b\u4e2d\u7684\u91cf\u5b50-\u7ecf\u5178\u8fc7\u6e21\u7684\u95ee\u9898[8]\u3002<\/span><\/section>\n

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\u56fe2 \u4e00\u4e2a\u57fa\u4e8e\u79bb\u6563\u80fd\u7ea7\u7cfb\u7edf\u7684\u91cf\u5b50\u70ed\u529b\u5b66\u5faa\u73af<\/span><\/section>\n<\/section>\n
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\u7136\u800c\uff0c\u57282007\u5e74\u4e4b\u524d\uff0c\u5173\u4e8e\u5355\u91cf\u5b50\u7cfb\u7edf\u7684\u70ed\u529b\u5b66\u7814\u7a76\u6bd4\u8f83\u7f3a\u4e4f\uff0c\u6709\u5173\u91cf\u5b50\u70ed\u529b\u5b66\u8fc7\u7a0b\u548c\u91cf\u5b50\u70ed\u529b\u5b66\u5faa\u73af\u7684\u6982\u5ff5\u8f83\u4e3a\u6df7\u4e71\u3002\u8003\u8651\u5230\u8fd9\u4e00\u72b6\u51b5\uff0c2007\u5e74\uff0c\u7b14\u8005\u53ca\u5408\u4f5c<\/span>\u8005[9]<\/span>\u7cfb\u7edf\u5730\u7814\u7a76\u4e86\u91cf\u5b50\u7cfb\u7edf\u7684\u70ed\u529b\u5b66\u8fc7\u7a0b\u548c\u70ed\u529b\u5b66\u5faa\u73af\uff0c\u6f84\u6e05\u4e86\u5305\u62ec\u91cf\u5b50\u7b49\u6e29\u8fc7\u7a0b\uff0c\u91cf\u5b50\u7b49\u5bb9\u8fc7\u7a0b\uff0c\u91cf\u5b50Carnot\u5faa\u73af\uff0c\u4ee5\u53ca\u91cf\u5b50Otto\u5faa\u73af\u7b49\u91cf\u5b50\u70ed\u529b\u5b66\u7684\u57fa\u672c\u6982\u5ff5\u3002\u8fd9\u65b9\u9762\u7684\u76f8\u5173\u5de5\u4f5c\u5728\u91cf\u5b50\u70ed\u529b\u5b66\u9886\u57df\u4ea7\u751f\u4e86\u8f83\u5927\u7684\u56fd\u9645\u5f71\u54cd\u3002\u4e0b\u6587\u5c06\u7b80\u8ff0\u7b14\u8005\u56e2\u961f\u5728\u8fd9\u4e00\u9886\u57df\u7684\u7814\u7a76\u6210\u679c\uff0c\u5176\u4e2d\u4e3b\u8981\u5305\u62ec\u5c06\u505a\u529f\u3001\u4f20\u70ed\u3001\u7b49\u6e29\u8fc7\u7a0b\u3001Carnot\u70ed\u673a\u3001Otto\u70ed\u673a\u7b49\u6982\u5ff5\u63a8\u5e7f\u5230\u5c0f\u91cf\u5b50\u7cfb\u7edf\u3002<\/span><\/section>\n

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2.1 \u91cf\u5b50\u70ed\u673a\u7814\u7a76<\/strong><\/span><\/section>\n

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\u8003\u8651\u4e00\u4e2a\u4efb\u610f\u591a\u80fd\u7ea7\u5355\u91cf\u5b50\u7cfb\u7edf<\/span> (\u89c1\u56fe3)<\/span>\u3002\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u8003\u8651\u7684\u7cfb\u7edf\u53ea\u5305\u542b\u79bb\u6563\u80fd\u7ea7\u7ed3\u6784\uff0c\u5e76\u4e14\u53ea\u542b\u6709\u6709\u9650\u4e2a\u672c\u5f81\u80fd\u7ea7\u3002\u5f53\u7136\uff0c\u4e5f\u53ef\u4ee5\u66f4\u4e00\u822c\u5730\u8003\u8651\u5177\u6709\u65e0\u7a77\u591a\u4e2a\u80fd\u7ea7\u7684\u7cfb\u7edf\u3002<\/span><\/section>\n

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\u5176\u4e2d\u03b4Q <\/em>=T<\/em>dS<\/em>\uff0c\u03b4W <\/em>=\u2211i<\/sub>Yi <\/sub><\/em>dyi <\/sub><\/em><\/span>[11]<\/span>\uff1bT <\/em>\u548cS<\/em>\u5206\u522b\u662f\u6e29\u5ea6\u548c\u71b5\uff1byi <\/sub><\/em>\u662f\u5e7f\u4e49\u5750\u6807\uff0cYi <\/sub><\/em>\u662f\u4e0eyi <\/sub><\/em>\u5171\u8f6d\u7684\u5e7f\u4e49\u529b\u3002\u8003\u8651\u5230von Neumann\u71b5S<\/em>\u548c\u5404\u4e2a\u672c\u5f81\u80fd\u7ea7En<\/sub><\/em>\u4e0a\u7684\u5e03\u5c45\u6570Pn<\/sub><\/em>\u7684\u5173\u7cfb<\/span> (k<\/em>B<\/sub>\u662fBoltzmann\u5e38\u6570)<\/span> \uff1a<\/span><\/section>\n

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\u65b9\u7a0b(6) \u610f\u5473\u7740\u201c\u505a\u529f\u201d\u76f8\u5e94\u4e8e\u672c\u5f81\u80fd\u7ea7En<\/sub><\/em>\u7684\u6539\u53d8\u3002\u8fd9\u4e00\u70b9\u4e0e\u53e6\u4e00\u4e2a\u5e38\u8bc6\u6027\u7684\u7ed3\u8bba\u4e00\u81f4\uff0c\u5373\u505a\u529f\u5fc5\u7136\u4f34\u968f\u7740\u7cfb\u7edf\u7684\u5e7f\u4e49\u5750\u6807\u7684\u6539\u53d8\u3002\u800c\u5728\u5355\u91cf\u5b50\u7cfb\u7edf\u4e2d\uff0c\u5e7f\u4e49\u5750\u6807\u7684\u6539\u53d8\u53c8\u5bfc\u81f4\u4e86\u7cfb\u7edf\u672c\u5f81\u80fd\u91cf\u7684\u6539\u53d8\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u65b9\u7a0b(6)\u548c(7)\u5173\u4e8e\u505a\u529f\u548c\u70ed\u4f20\u9012\u5728\u5355\u91cf\u5b50\u7cfb\u7edf\u7684\u8868\u8ff0\uff0c\u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\u5728\u5355\u91cf\u5b50\u7cfb\u7edf\u7684\u8868\u8ff0dU <\/em>=\u03b4Q <\/em>+\u03b4W<\/em>\u5c31\u53ef\u4ee5\u4ece\u65b9\u7a0b(4)\u5f97\u5230\u3002\u9700\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u57fa\u4e8e\u65b9\u7a0b(6)\u548c\u65b9\u7a0b(7)\u5173\u4e8e\u505a\u529f\u548c\u4f20\u70ed\u7684\u5b9a\u4e49\uff0c\u53ef\u4ee5\u5efa\u7acb\u4e00\u5957\u81ea\u6d3d\u7684\u7edf\u8ba1\u70ed\u529b\u5b66\u7406\u8bba\u3002\u5728\u8fd9\u4e2a\u7406\u8bba\u4f53\u7cfb\u91cc\u9762\uff0c\u538b\u5f3ap<\/em>\u548c\u4f53\u79efV<\/em>\u4e0d\u518d\u662f\u57fa\u672c\u7684\uff0c\u4e5f\u4e0d\u518d\u662f\u5fc5\u9700\u7684\u53c2\u6570\u3002\u800c{En<\/sub><\/em>}\u548c{Pn<\/sub><\/em>}\u624d\u662f\u5efa\u7acb\u7edf\u8ba1\u70ed\u529b\u5b66\u7406\u8bba\u6240\u5fc5\u9700\u7684\u5143\u7d20\u3002\u53ef\u4ee5\u5728\u67d0\u4e9b\u65e0\u6cd5\u5b9a\u4e49\u538b\u5f3a\u548c\u4f53\u79ef\u7684\u7cfb\u7edf\uff0c\u6bd4\u5982\u4e00\u4e2a\u8c10\u632f\u5b50\u6216\u8005\u4e00\u4e2a\u4e8c\u80fd\u7ea7\u7cfb\u7edf\u5229\u7528\u65b9\u7a0b(6)\u548c\u65b9\u7a0b(7)\u5efa\u7acb\u81ea\u6d3d\u7684\u7edf\u8ba1\u70ed\u529b\u5b66\u7406\u8bba\u3002\u5f53\u7136\uff0c\u5bf9\u4e8e\u53ef\u4ee5\u660e\u786e\u5b9a\u4e49\u538b\u5f3a\u548c\u4f53\u79ef\u7684\u7cfb\u7edf\uff0c\u6bd4\u5982\u6d3b\u585e\u4e2d\u7684\u6c14\u4f53\uff0c\u65b9\u7a0b(6)\u548c\u65b9\u7a0b(7)\u7ed9\u51fa\u7684\u505a\u529f\u548c\u4f20\u70ed\u7684\u5b9a\u4e49\u4e0e\u03b4Q <\/em>=T<\/em>dS<\/em>, \u03b4W <\/em>=\u2212p<\/em>dV<\/em>\u4e00\u81f4\u3002\u7531\u6b64\u53ef\u89c1\u65b9\u7a0b(6)\u548c\u65b9\u7a0b(7)\u662f\u66f4\u4e00\u822c\u7684\u3001\u6bd4\u03b4<\/em>Q <\/em>=T<\/em>dS<\/em>, \u03b4W <\/em>=\u2212p<\/em>dV<\/em>\u9002\u7528\u8303\u56f4\u66f4\u5e7f\u7684\u5173\u4e8e\u505a\u529f\u548c\u4f20\u70ed\u7684\u5b9a\u4e49\u3002\u6b64\u5916\uff0c\u8fd8\u9700\u8981\u5f3a\u8c03\uff0c\u7ecf\u5178\u7cfb\u7edf\u7684\u70ed\u4f20\u9012\u8868\u8fbe\u5f0f\u03b4<\/em>Q <\/em>=T<\/em>dS<\/em>, \u03b4W <\/em>= \u2211i<\/sub>Yi <\/sub><\/em>dyi <\/sub><\/em>\u4ec5\u4ec5\u9002\u7528\u4e8e\u51c6\u9759\u6001\u8fc7\u7a0b\u3002\u4e0e\u4e4b\u4e00\u81f4\u7684\u662f\uff0c\u91cf\u5b50\u7cfb\u7edf\u7684\u505a\u529f\u548c\u4f20\u70ed\u7684\u65b9\u7a0b(6)\u548c\u65b9\u7a0b(7)\u4e5f\u53ea\u9002\u7528\u4e8e\u51c6\u9759\u6001\u8fc7\u7a0b\u3002\u57282007\u5e74\u4e4b\u524d\u7684\u6587\u732e[7,15]\u4e2d\uff0c\u5173\u4e8e\u91cf\u5b50\u70ed\u673a<\/span> (\u6bd4\u5982\u91cf\u5b50Carnot\u70ed\u673a\u548c\u91cf\u5b50Otto\u70ed\u673a) <\/span>\u7684\u5b9a\u4e49\u5e76\u4e0d\u4e00\u81f4\uff0c\u6709\u7684\u751a\u81f3\u4e92\u76f8\u77db\u76fe\u3002\u56e0\u6b64\u91cf\u5b50Carnot\u70ed\u673a\u548c\u91cf\u5b50Otto\u70ed\u673a\u7684\u6027\u8d28\u96be\u4ee5\u6e05\u6670\u9610\u660e\u3002\u8fd9\u79cd\u60c5\u51b5\u4fc3\u4f7f\u6211\u4eec\u4e3a\u5404\u79cd\u91cf\u5b50\u70ed\u673a\u5faa\u73af\u63d0\u51fa\u666e\u9002\u7684\u5b9a\u4e49\u3002\u4efb\u4f55\u4e00\u4e2a\u91cf\u5b50\u70ed\u673a\u7684\u5faa\u73af\u90fd\u662f\u7531\u82e5\u5e72\u57fa\u672c\u7684\u91cf\u5b50\u70ed\u529b\u5b66\u8fc7\u7a0b\u7ec4\u6210\u7684\u3002\u6709\u4e86\u5355\u91cf\u5b50\u7cfb\u7edf\u505a\u529f\u548c\u4f20\u70ed\u7684\u5b9a\u4e49\uff0c\u5c31\u53ef\u4ee5\u7814\u7a76\u5355\u91cf\u5b50\u7cfb\u7edf\u7684\u70ed\u673a\u5faa\u73af\u3002\u4e0b\u6587\u5c06\u63cf\u8ff0<\/span> (\u7531\u8fd9\u4e9b\u91cf\u5b50\u70ed\u529b\u5b66\u8fc7\u7a0b\u6784\u6210\u7684) <\/span>\u5e73\u8861\u6001\u70ed\u529b\u5b66\u5faa\u73af\u7684\u6027\u8d28\uff0c\u540c\u65f6\u5c06\u91cf\u5b50\u70ed\u673a\u7684\u6027\u8d28\u4e0e\u7ecf\u5178\u70ed\u673a\u7684\u6027\u8d28\u8fdb\u884c\u6bd4\u8f83\u3002<\/span><\/section>\n

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\u7ecf\u5178Carnot\u70ed\u673a\u662f\u4e00\u79cd\u975e\u5e38\u5178\u578b\u7684\u70ed\u673a\uff0c\u5176\u6bcf\u4e2a\u5faa\u73af\u76844\u4e2a\u51b2\u7a0b\u7684\u70ed\u529b\u5b66\u6027\u8d28\u90fd\u975e\u5e38\u6e05\u6670\uff0c\u800c\u4e14\u5b83\u4ee3\u8868\u4e86\u4e00\u7c7b\u666e\u9002\u7684\u53ef\u9006\u70ed\u673a\u7684\u7269\u7406\u673a\u5236\u3002\u76ee\u524d\uff0c\u5173\u4e8e\u91cf\u5b50\u70ed\u673a\u7684\u7814\u7a76\u5927\u591a\u96c6\u4e2d\u5728\u5bf9\u7ecf\u5178Carnot\u70ed\u673a\u7684\u91cf\u5b50\u529b\u5b66\u63a8\u5e7f\u65b9\u9762\uff0c\u4e5f\u5c31\u662f\u5bf9\u91cf\u5b50Carnot\u70ed\u673a\u6709\u5173\u65b9\u9762\u7684\u7814\u7a76\u3002<\/span><\/section>\n

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\u91cf\u5b50Carnot\u70ed\u673a<\/span> (\u4e00\u4e2a\u57fa\u4e8e\u4e8c\u80fd\u7ea7\u7cfb\u7edf\u7684\u91cf\u5b50Carnot\u70ed\u673a\u5faa\u73af\u7684\u793a\u610f\u56fe\u89c1\u56fe4)<\/span>\uff0c\u5982\u540c\u4e0e\u5176\u5bf9\u5e94\u7684\u7ecf\u5178Carnot\u70ed\u673a\u4e00\u6837\uff0c\u7531\u4e24\u4e2a(\u91cf\u5b50)\u7b49\u6e29\u8fc7\u7a0bA\u2192B\u53ca C\u2192D\u548c\u4e24\u4e2a<\/span> (\u91cf\u5b50) <\/span>\u7edd\u70ed\u8fc7\u7a0bB\u2192C\u53caD\u2192A\u6784\u6210\u3002\u5728\u7b49\u6e29\u81a8\u80c0\u8fc7\u7a0bA\u2192B\u4e2d\uff0c\u5de5\u4f5c\u7269\u8d28\uff0c\u5373\u88ab\u675f\u7f1a\u5728\u52bf\u9631\u4e2d\u7684\u4e00\u4e2a\u7c92\u5b50\u59cb\u7ec8\u4e0e\u4e00\u4e2a\u6e29\u5ea6\u4e3aT<\/em>h<\/sub>\u7684\u70ed\u6e90\u76f8\u63a5\u89e6\u3002\u5de5\u4f5c\u7269\u8d28\u7684\u80fd\u7ea7\u6539\u53d8\u7684\u901f\u5ea6\u6bd4\u7cfb\u7edf\u7684\u5f1b\u8c6b\u901f\u5ea6\u6162\u5f97\u591a\uff0c\u4ee5\u81f3\u4e8e\u8fd9\u4e2a\u7c92\u5b50\u4e00\u76f4\u4e0e\u70ed\u5e93\u4fdd\u6301\u5728\u70ed\u5e73\u8861\u72b6\u6001\u3002<\/span><\/section>\n

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\n
<\/section>\n<\/section>\n
\n
\u56fe4 \u4e00\u4e2a\u57fa\u4e8e\u4e8c\u80fd\u7ea7\u91cf\u5b50\u7cfb\u7edf\u7684\u91cf\u5b50Carnot\u70ed\u673a\u5faa\u73af\uff0cT<\/em>h<\/sub>\u548cT<\/em>l<\/sub>\u5206\u522b\u4ee3\u8868\u9ad8\u6e29\u548c\u4f4e\u6e29\u70ed\u5e93\u7684\u6e29\u5ea6\uff0c\u0394<\/em>\u548cP<\/em>e<\/sub>\u4ee3\u8868\u4e8c\u80fd\u7ea7\u7cfb\u7edf\u7684\u80fd\u7ea7\u5dee\u548c\u6fc0\u53d1\u6001\u4e0a\u7684\u5e03\u5c45\u6570\uff0cP<\/em>\u548cV<\/em>\u4ee3\u8868\u7ecf\u5178\u7406\u60f3\u6c14\u4f53\u7684\u538b\u5f3a\u548c\u4f53\u79ef<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n
\n
\u8981\u4f7f\u91cf\u5b50\u70ed\u673a\u5bf9\u5916\u505a\u6b63\u529f\uff0c\u70ed\u673a\u7684\u4e24\u4e2a\u70ed\u5e93\u5fc5\u987b\u6ee1\u8db3\u6761\u4ef6T<\/em>h<\/sub>>T<\/em>l<\/sub>\u3002\u8fd9\u4e2a\u5bf9\u91cf\u5b50Carnot\u70ed\u673a\u7684\u9650\u5236\u4e5f\u5c31\u662f\u6240\u8c13\u7684\u91cf\u5b50Carnot\u70ed\u673a\u7684\u201c\u6b63\u529f\u6761\u4ef6\u201d\uff0c\u548c\u7ecf\u5178Carnot\u70ed\u673a\u7684\u201c\u6b63\u529f\u6761\u4ef6\u201d\u662f\u4e00\u6837\u7684\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u8bf4\u660e\u5b9a\u4e49\u7684\u91cf\u5b50Carnot\u70ed\u673a\u662f\u7ecf\u5178Carnot\u70ed\u673a\u7684\u91cf\u5b50\u529b\u5b66\u5bf9\u5e94\uff0c\u5728\u56fe4(c)\uff0c(d)\u4e2d\u7ed9\u51fa\u4e86\u91cf\u5b50\u548c\u7ecf\u5178Carnot\u70ed\u673a\u5faa\u73af\u7684\u6e29\u5ea6-\u71b5\u5faa\u73af (T<\/em>–S<\/em>) \u56fe\u3002\u4ece\u56fe\u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u7ecf\u5178\u548c\u91cf\u5b50\u7684Carnot\u5faa\u73af\u7684T<\/em>–S<\/em>\u56fe\u5177\u6709\u5b8c\u5168\u76f8\u540c\u7684\u5f62\u5f0f\u3002\u57fa\u4e8e\u4e0a\u8ff0\u7406\u7531\uff0c\u53ef\u63a8\u65ad\u672c\u6587\u7ed9\u51fa\u7684\u91cf\u5b50 Carnot \u70ed\u673a\u5faa\u73af\u662f\u7ecf\u5178 Carnot \u70ed\u673a\u5faa\u73af\u7684\u91cf\u5b50\u529b\u5b66\u5bf9\u5e94\u3002<\/span><\/section>\n

<\/section>\n
\u91cf\u5b50Otto\u70ed\u673a\u5faa\u73af\u662f\u53e6\u4e00\u7c7b\u5f88\u91cd\u8981\u7684\u91cf\u5b50\u70ed\u673a\u5faa\u73af\uff0c\u5176\u4e5f\u5f15\u8d77\u4e86\u5f88\u591a\u5173\u6ce8\u3002\u4e0eCarnot\u5faa\u73af\u7c7b\u4f3c\uff0c\u7ecf\u5178Otto\u5faa\u73af\u7684\u91cf\u5b50\u529b\u5b66\u5bf9\u5e94\u4e5f\u6709\u5f88\u591a\u7814\u7a76[9]\u3002\u5b9e\u9645\u4e0a\uff0c\u6c7d\u8f66\u7684\u5185\u71c3\u673a\u6240\u8fdb\u884c\u7684\u5faa\u73af\u5c31\u662f\u7ecf\u5178Otto\u5faa\u73af <\/span>(\u800c\u975e\u7ecf\u5178Carnot\u5faa\u73af)<\/span>\u3002Otto\u5faa\u73af\u7531\u4e24\u4e2a\u7ecf\u5178\u7684\u7b49\u5bb9\u8fc7\u7a0b\u548c\u4e24\u4e2a\u7ecf\u5178\u7684\u7edd\u70ed\u8fc7\u7a0b\u6784\u6210\u3002\u91cf\u5b50Otto\u5faa\u73af\u7531\u4e24\u4e2a\u91cf\u5b50\u7b49\u5bb9\u8fc7\u7a0b\u548c\u4e24\u4e2a\u91cf\u5b50\u7edd\u70ed\u8fc7\u7a0b\u7ec4\u6210\u3002\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u6587\u732e[1]\u4e2d\u63d0\u5230\u7684\u7b2c1\u4e2a\u91cf\u5b50\u70ed\u673a\u6a21\u578b\u4e8b\u5b9e\u4e0a\u662f\u4e00\u4e2a\u91cf\u5b50Otto\u70ed\u673a\u6a21\u578b\u3002\u56e0\u4e3a\u5b83\u7684\u70ed\u673a\u6548\u7387\u548c\u6b63\u529f\u6761\u4ef6\u5206\u522b\u662f1\u2212\u0394<\/em>1<\/sub>\/\u0394<\/em>0<\/sub>\u548cT<\/em>h<\/sub>>(\u0394<\/em>0<\/sub>\/\u0394<\/em>1<\/sub>)T<\/em>l<\/sub>\uff0c\u5176\u4e2d\u0394<\/em>1<\/sub>\u53ca\u0394<\/em>0<\/sub>\u5206\u522b\u662f\u5de5\u4f5c\u7269\u8d28\u7684\u4e24\u4e2a\u80fd\u7ea7\u5dee\uff0cT<\/em>h<\/sub>\u548cT<\/em>l<\/sub>\u5206\u522b\u662f\u4e24\u4e2a\u70ed\u5e93\u7684\u6e29\u5ea6\u3002<\/span><\/section>\n

<\/section>\n
\u4ece\u7814\u7a76\u7ed3\u679c\u53ef\u4ee5\u770b\u51fa\uff0c\u5c3d\u7ba1\u91cf\u5b50\u5c5e\u6027\u4f1a\u5e26\u6765\u4e00\u4e9b\u6709\u522b\u4e8e\u7ecf\u5178\u7684\u7279\u5f81\uff0c\u4f46\u662f\u57fa\u4e8e\u5355\u91cf\u5b50\u7cfb\u7edf\u7684\u91cf\u5b50\u70ed\u673a\u7684\u6027\u80fd\u5e76\u6ca1\u6709\u8d85\u8d8a\u7ecf\u5178\u70ed\u673a\u3002\u800c\u5728\u91cf\u5b50\u4fe1\u606f\u9886\u57df\uff0c\u91cf\u5b50\u4fe1\u606f\u5904\u7406\u76f8\u6bd4\u4e8e\u7ecf\u5178\u4fe1\u606f\u5904\u7406\u5177\u6709\u663e\u8457\u7684\u4f18\u52bf\uff0c\u4e24\u8005\u5f62\u6210\u4e86\u9c9c\u660e\u7684\u5bf9\u6bd4\u3002<\/span><\/section>\n

<\/section>\n
2.2 Maxwell \u5996\u4e0e\u4fe1\u606f\u201c\u5236\u51b7\u673a\u201d<\/strong><\/span><\/section>\n

<\/section>\n
1860\u5e74\u5de6\u53f3\uff0cClausius\u548cKelvin\u72ec\u7acb\u63d0\u51fa\u4e86\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u3002\u4e4b\u540e\u4e0d\u5c11\u7269\u7406\u5b66\u5bb6\u66fe\u4e00\u5ea6\u5bf9\u5176\u666e\u9002\u6027\u6301\u6709\u6000\u7591\u6001\u5ea6\u3002\u4e00\u4e9b\u7814\u7a76\u8005\u63d0\u51fa\u5404\u79cd\u201c\u53cd\u4f8b\u201d\uff0c\u8bd5\u56fe\u8bf4\u660e\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u53ef\u80fd\u8fdd\u53cd\u6982\u7387\u6027\u3002\u5176\u4e2d\u4e00\u4e2a\u91cd\u8981\u7684\u4f8b\u5b50\u662f\u7269\u7406\u5b66\u5bb6Maxwell\u57281871\u5e74\u63d0\u51fa\u6765\u7684\u4e00\u4e2a\u601d\u60f3\u5b9e\u9a8c\u3002\u540e\u6765\u8fd9\u4e2a\u601d\u60f3\u5b9e\u9a8c\u4e2d\u7684\u5047\u60f3\u667a\u6167\u751f\u547d\u88ab\u5f00\u5c14\u6587\u547d\u540d\u4e3aMaxwell\u5996\uff0c\u5e76\u4e14\u5f15\u8d77\u4e86\u5f88\u591a\u7269\u7406\u5b66\u5bb6\u7684\u5174\u8da3\u3002\u591a\u4f4d\u7269\u7406\u5b66\u5bb6\u524d\u8d74\u540e\u7ee7\u6295\u5165\u5927\u91cf\u7cbe\u529b\u53bb\u7814\u7a76\u8fd9\u4e2a\u601d\u60f3\u5b9e\u9a8c\uff0c\u4ee5\u53ca\u5176\u4e0e\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u53ef\u80fd\u77db\u76fe\u7684\u65b9\u9762[16]\u3002\u5bf9Maxwell\u5996\u7684\u7814\u7a76\u6301\u7eed\u4e86\u4e00\u767e\u591a\u5e74\u3002\u76f4\u52301982\u5e74\uff0c\u8fd9\u4e2a\u56f0\u6270\u7269\u7406\u5b66\u754c\u4e00\u4e2a\u591a\u4e16\u7eaa\u7684\u96be\u9898\u624d\u6700\u7ec8\u88ab\u7269\u7406\u5b66\u5bb6Bennett\u5229\u7528Landauer\u539f\u7406<\/span> (Landauer\u5728\u7814\u7a76\u8ba1\u7b97\u80fd\u8017\u65f6\u63d0\u51fa\u7684) <\/span>\u89e3\u51b3\u3002\u4e0b\u6587\u5c06\u7b80\u8ff0\u8fd9\u6bb5\u70ed\u529b\u5b66\u53d1\u5c55\u53f2\u4e0a\u8457\u540d\u7684\u601d\u60f3\u5b9e\u9a8c\uff0c\u5e76\u4ecb\u7ecd\u6211\u4eec\u5728\u8fd9\u4e2a\u9886\u57df\u7684\u4e00\u4e9b\u5de5\u4f5c\u3002<\/span><\/section>\n

<\/section>\n
Maxwell\u5996<\/span><\/strong>\u662f\u4e00\u79cd\u80fd\u591f\u533a\u5206\u5355\u4e2a\u6c14\u4f53\u5206\u5b50\u901f\u5ea6\u7684\u5047\u60f3\u7269<\/span> (\u89c1\u56fe5(i))<\/span>\uff0c\u5b83\u80fd\u591f\u8ba9\u4e00\u4e2a\u5bb9\u5668\u5185\u8fd0\u52a8\u5feb<\/span> (\u201c\u70ed\u201d) <\/span>\u7684\u5206\u5b50\u548c\u8fd0\u52a8\u6162 <\/span>(\u201c\u51b7\u201d) <\/span>\u7684\u5206\u5b50\u5206\u522b\u5360\u636e\u4e0d\u540c\u7684\u533a\u57df\uff0c\u4ece\u800c\u4f7f\u5bb9\u5668\u4e2d\u4e0d\u540c\u533a\u57df\u7684\u6e29\u5ea6\u4e0d\u540c[16]\u3002\u8fd9\u4e2a\u7ed3\u8bba\u4f3c\u4e4e\u4e0e\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u76f8\u8fdd\u80cc\uff1a\u5f53\u628a\u9ad8\u6e29\u548c\u4f4e\u6e29\u5206\u5b50\u96c6\u5408\u5f53\u6210\u4e24\u4e2a\u70ed\u6e90\uff0c\u5728\u5b83\u4eec\u4e4b\u95f4\u653e\u7f6e\u7684\u70ed\u673a\uff0c\u80fd\u591f\u5229\u7528\u6e29\u5dee\u5bf9\u5916\u505a\u529f\u3002\u6574\u4f53\u6765\u770b\uff0cMaxwell\u5996\u7684\u5f15\u8fdb\uff0c\u4f7f\u5f97\u201c\u4ece\u5355\u4e00\u70ed\u6e90\u5438\u70ed\u5b8c\u5168\u8f6c\u5316\u4e3a\u5bf9\u5916\u505a\u529f\u201d\u6210\u4e3a\u53ef\u80fd\uff0c\u4ece\u800c\u51fa\u73b0\u4e86\u8fdd\u53cd\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u7b2c\u4e8c\u7c7b\u6c38\u52a8\u673a\u3002\u8fd9\u5c31\u662f\u201cMaxwell\u5996\u4f6f\u8c2c\u201d\u3002\u5728\u76f8\u5f53\u957f\u7684\u65f6\u95f4\u5185\uff0c\u7269\u7406\u5b66\u5bb6\u4eec\u6ca1\u6709\u80fd\u591f\u5bf9\u201cMaxwell\u5996\u4f6f\u8c2c\u201d\u7ed9\u51fa\u4e00\u4e2a\u5f88\u6ee1\u610f\u7684\u89e3\u91ca\u3002\u8fd9\u4e2a\u95ee\u9898\u7684\u4e00\u4e2a\u91cd\u8981\u7684\u8fdb\u5c55\u662f1929\u5e74\u7269\u7406\u5b66\u5bb6Szilard[17]\u5f15\u5165\u7684\u5355\u5206\u5b50\u70ed\u673a\u6a21\u578b<\/span> (\u89c1\u56fe5(ii))<\/span>\u3002\u5728\u8fd9\u4e2a\u7b80\u5316\u4e86\u7684Maxwell\u5996\u70ed\u673a\u6a21\u578b\u4e2d\uff0cSzilard\u9996\u6b21\u5c06\u4fe1\u606f\u7684\u6982\u5ff5\u5f15\u5165\u5230\u70ed\u529b\u5b66\u5faa\u73af\u4e2d\u3002\u4ed6\u76f4\u89c2\u5730\u8ba4\u4e3a\uff0cMaxwell\u5996\u6d4b\u91cf\u5206\u5b50\u5904\u4e8e\u5de6\u8fb9\u8fd8\u662f\u53f3\u8fb9\u662f\u4e00\u4e2a\u83b7\u53d6\u4fe1\u606f\u7684\u8fc7\u7a0b\uff0c\u53ef\u80fd\u4f1a\u6d88\u8017\u80fd\u91cf\uff0c\u4ece\u800c\u5bfc\u81f4\u6574\u4f53\u7684\u71b5\u589e\u5927\u3002\u5982\u679c\u628a\u8fd9\u4e2a\u6d88\u8017\u5305\u542b\u5230\u70ed\u529b\u5b66\u5faa\u73af\u4e2d\u6765\uff0c\u5c31\u4e0d\u8fdd\u53cd\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\uff0cMaxwell\u5996\u4f6f\u8c2c\u4e5f\u5c31\u8fce\u5203\u800c\u89e3\u3002<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n
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<\/section>\n<\/section>\n
\n
\u56fe5 Maxwell\u5996\u548cSzilard\u5355\u5206\u5b50\u70ed\u673a\u6a21\u578b<\/span><\/section>\n<\/section>\n
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1982\u5e74Bennett[19]\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u867d\u7136\u8bf4\u660eMaxwell\u5996\u4e0d\u4f1a\u5bf9\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u6784\u6210\u5a01\u80c1\uff0c\u5373\u64e6\u9664\u5176\u5b58\u50a8\u5355\u5143\u7684\u4fe1\u606f\uff0c\u4fdd\u8bc1\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u4e0d\u4f1a\u88ab\u8fdd\u53cd\uff0c\u4f46\u662f\u4ed6\u7684\u5047\u60f3\u5b9e\u9a8c\u4f3c\u4e4e\u4ecd\u7136\u6ca1\u6709\u5b8c\u5168\u6446\u8131\u201c\u667a\u6167\u7cbe\u7075\u201d\u8fd9\u4e2a\u5047\u8bbe\u3002\u6709\u201c\u667a\u6167\u7cbe\u7075\u201d\u53c2\u4e0e\u7684<\/span> (\u975e\u81ea\u52a8\u5316\u7684) <\/span>\u4fe1\u606f\u70ed\u673a\u6a21\u578b\u4e0d\u53ef\u80fd\u5728\u5b9e\u9a8c\u5ba4\u5b9e\u73b0\uff0c\u56e0\u4e3a\u4e16\u754c\u4e0a\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u201c\u667a\u6167\u7cbe\u7075\u201d\u3002\u90a3\u4e48\uff0c\u662f\u5426\u6709\u53ef\u80fd\u8bbe\u8ba1\u4e00\u4e2a\u5b8c\u5168\u81ea\u52a8\u5316\u7684Maxwell\u70ed\u673a\u6216Maxwell\u5236\u51b7\u673a\uff1f\u5373\u6ca1\u6709\u4efb\u4f55\u201c\u667a\u6167\u7cbe\u7075\u201d\u7684\u53c2\u4e0e\uff0c\u8fd9\u4e2a\u673a\u5668\u80fd\u591f\u5b9e\u73b0Maxwell\u6700\u521d\u7684\u8bbe\u60f3\uff0c\u5e76\u4e14\u5f97\u5230\u548cLandauer\u539f\u7406\u9884\u8a00\u76f8\u4e00\u81f4\u7684\u7ed3\u679c\u3002\u5982\u679c\u80fd\u591f\u6784\u9020\u51fa\u4e00\u4e2a\u81ea\u52a8\u5316\u7684\u4fe1\u606f\u70ed\u673a\u6a21\u578b\uff0c\u5c06\u6709\u5e0c\u671b\u5728\u5b9e\u9a8c\u5ba4\u4e2d\u771f\u6b63\u5236\u9020\u51fa\u4e00\u4e2a\u4fe1\u606f\u70ed\u673a\u6216\u4fe1\u606f\u64e6\u9664\u5668\uff0c\u4ece\u800c\u5b9e\u73b0Maxwell\u6700\u521d\u7684\u8bbe\u60f3\u3002\u8fd9\u4e2a\u88c5\u7f6e\u4e0d\u4ec5\u53ef\u4ee5\u5e2e\u52a9\u7406\u89e3\u4fe1\u606f\u3001\u71b5\u3001\u70ed\u3001\u529f\u8fd9\u4e9b\u7269\u7406\u5b66\u57fa\u672c\u6982\u5ff5\uff0c\u8fd8\u5177\u6709\u5f88\u91cd\u8981\u7684\u5e94\u7528\u524d\u666f\u30022013\u5e74Mandal\u7b49[26]\u8003\u8651\u4e86\u4e00\u4e2a\u81ea\u52a8\u5316\u7684\u4fe1\u606f\u5236\u51b7\u673a\u6a21\u578b\u3002\u4e0e\u4fe1\u606f\u70ed\u673a\u7c7b\u4f3c\uff0c\u8fd9\u4e2a\u81ea\u52a8\u5316\u7684\u6a21\u578b\u901a\u8fc7\u6d88\u8d39\u8f93\u5165\u7684\u5b58\u50a8\u5355\u5143\u5229\u7528\u70ed\u6da8\u843d\u5c06\u70ed\u91cf\u4ece\u4f4e\u6e29\u70ed\u5e93\u8f93\u9001\u5230\u9ad8\u6e29\u70ed\u5e93\uff0c\u6216\u8005\u76f8\u53cd\u901a\u8fc7\u6d88\u8d39\u9ad8\u6e29\u70ed\u5e93\u7684\u70ed\u91cf\uff0c\u5b9e\u73b0\u5bf9\u5b58\u50a8\u5355\u5143\u4e0a\u4fe1\u606f\u7684<\/span> (\u90e8\u5206) <\/span>\u64e6\u9664\u3002\u8fd9\u4e2a\u6a21\u578b\u771f\u6b63\u4f53\u73b0\u4e86Maxwell\u57281871\u5e74\u63d0\u51fa\u7684\u601d\u60f3\u5b9e\u9a8c\u7684\u5185\u6db5\u3002\u6709\u5173\u8fd9\u4e2a\u6a21\u578b\u7684\u66f4\u8be6\u7ec6\u7684\u60c5\u51b5\u8bf7\u53c2\u9605\u6587\u732e[26]\u3002<\/span><\/section>\n<\/section>\n
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\u5f53\u7cfb\u7edf\u504f\u79bb\u70ed\u529b\u5b66\u6781\u9650\u65f6\uff0c\u5c0f\u7cfb\u7edf\u7684\u70ed\u529b\u5b66\u91cf\u7684\u5e73\u5747\u503c\u4e0d\u8db3\u4ee5\u63cf\u8ff0\u7cfb\u7edf\u7684\u5168\u90e8\u884c\u4e3a\uff0c\u6b64\u65f6\u6da8\u843d\u53d8\u5f97\u81f3\u5173\u91cd\u8981\u3002\u4e8b\u5b9e\u4e0a\uff0c\u70ed\u529b\u5b66\u91cf\u7684\u6da8\u843d\u8574\u542b\u4e86\u4e30\u5bcc\u7684\u975e\u5e73\u8861\u8fc7\u7a0b\u7684\u4fe1\u606f\uff0c\u5bf9\u70ed\u529b\u5b66\u91cf\u6da8\u843d\u7684\u7814\u7a76\u6df1\u5316\u4e86\u5bf9\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u7406\u89e3\u30021961\u5e74Feynman\u63d0\u51fa\u4e00\u4e2a\u601d\u60f3\u5b9e\u9a8c\uff0c\u5373Feynman\u68d8\u8f6e\u7684\u88c5\u7f6e <\/span>(\u89c1\u56fe6)<\/span>\u3002\u5982\u679c\u53ea\u8003\u8651\u70ed\u529b\u5b66\u91cf\u7684\u5e73\u5747\u884c\u4e3a\uff0c\u800c\u4e0d\u8003\u8651\u6da8\u843d\uff0c\u5c31\u65e0\u6cd5\u7406\u89e3Feynman\u68d8\u8f6e\u7684\u5de5\u4f5c\u539f\u7406\u3002\u8003\u5bdf\u8fd9\u4e00\u7cfb\u7edf\u7684\u80fd\u91cf\u8f6c\u5316\u65f6\uff0c\u4f20\u7edf\u529f\u548c\u70ed\u7684\u5b9a\u4e49\u5df2\u7136\u5931\u6548\u30021997\u5e74\uff0cSekimoto[27]\u5728\u7814\u7a76Feynman\u68d8\u8f6e\u7cfb\u7edf\u65f6\u9996\u6b21\u5c06\u529f\u548c\u70ed\u5b9a\u4e49\u5728\u4e86\u5355\u6761\u968f\u673a\u8f68\u9053\u4e4b\u4e0a<\/span> (\u51e0\u4e4e\u5728\u540c\u65f6\uff0cJarzynski[28]\u72ec\u7acb\u5f15\u5165\u4e86\u8f68\u9053\u529f\u7684\u6982\u5ff5\uff0c\u4e0eSekimoto\u5f15\u5165\u7684\u8f68\u9053\u529f\u5b9a\u4e49\u4e00\u81f4)<\/span>\uff0c\u76f4\u63a5\u50ac\u751f\u4e86\u968f\u673a\u70ed\u529b\u5b66\u8fd9\u4e2a\u9886\u57df\u3002<\/span><\/section>\n<\/section>\n

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\u56fe6 Feynman\u68d8\u8f6e\uff0cT<\/em>A<\/sub>\u548cT<\/em>B<\/sub>\u4ee3\u8868\u4e24\u4e2a\u70ed\u5e93\u7684\u6e29\u5ea6\uff0c\u6709\u5173Feynman\u68d8\u8f6e\u7684\u4ecb\u7ecd\u53ef\u53c2\u8003\u6587\u732e[27]<\/span><\/p>\n<\/section>\n


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(8)\u5f0f\u662f\u63cf\u8ff0\u5e03\u6717\u7c92\u5b50\u5728\u76f8\u7a7a\u95f4(x<\/em>,v<\/em>)\u7684\u968f\u673a\u8f68\u9053\u968f\u65f6\u95f4t<\/em>\u7684\u6f14\u5316\u65b9\u7a0b\uff0c\u5176\u4e2dx<\/em>\u4e3a\u4f4d\u7f6e\uff0cv<\/em>\u4e3a\u901f\u5ea6\u3002(8)\u5f0f\u4e2dm<\/em>\u4e3a\u7c92\u5b50\u7684\u8d28\u91cf\uff0c\u03b3<\/em>\u4e3aStokes\u9ecf\u6ede\u7cfb\u6570\uff0c\u03b2 <\/em>=k<\/em>B<\/sub>T <\/em>\u22121<\/sup>\u4e3a\u6e29\u5ea6\u5012\u6570\uff0cF<\/em>(x<\/em>,t<\/em>)\u4ee3\u8868\u52bf\u573a\u529bF<\/em>(x<\/em>,t<\/em>)\u2008=\u2212\u2202<\/em>U<\/em>(x<\/em>,\u03bb<\/em>(t<\/em>))\/\u2202x<\/em>\uff0c\u5176\u4e2dU<\/em>(x<\/em>,\u03bb<\/em>(t<\/em>))\u4ee3\u8868\u52bf\u573a\u3002(8)\u5f0f\u4e2d\u901f\u5ea6\u65b9\u7a0b\u7684\u6700\u540e\u4e00\u9879\u4ee3\u8868\u968f\u673a\u529b\uff0c\u5176\u4e2d\u03be<\/em>(t<\/em>)\u662f\u5f52\u4e00\u5316\u7684\u767d\u566a\u58f0\uff0c\u6ee1\u8db3\u27e8\u03be<\/em>(t<\/em>)\u27e9= 0\uff0c\u27e8\u03be<\/em>(t<\/em>)\u03be<\/em>(t<\/em>\u2032)\u27e9=\u03b4<\/em>(t<\/em>\u2212t<\/em>\u2032)\uff0c\u5176\u4e2d\u5c16\u62ec\u53f7\u4ee3\u8868\u5e73\u5747\u7684\u542b\u4e49\u3002<\/span><\/section>\n

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\u7cfb\u7edf\u7684\u54c8\u5bc6\u987f\u91cf\u4e3a<\/span><\/section>\n

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\u5176\u4e2dz<\/em>=(x<\/em>,v<\/em>)\u4e3a\u76f8\u7a7a\u95f4\u5750\u6807\u3002<\/span><\/section>\n

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\u6709\u4e86\u529f\u3001\u70ed\u548c\u71b5\u4ea7\u751f<\/span>\u7684\u5b9a\u4e49\uff0c<\/span>\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u4e5f\u53ef\u4ee5\u88ab\u91cd\u65b0\u8868\u8ff0\u3002\u5728\u5c0f\u7cfb\u7edf\u4e2d\uff0c\u7531\u4e8e\u6709\u6da8\u843d\u7684\u5b58\u5728\uff0c\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u5c06\u53ea\u4f1a\u5728\u7edf\u8ba1\u5e73\u5747\u7684\u610f\u4e49\u4e0a\u6210<\/span>\u7acb[29,32]<\/span>\uff1a<\/span><\/section>\n

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\u9664\u4e86\u4ee5\u4e0a\u8f68\u9053\u529f\u3001\u70ed\u3001\u71b5\u4ea7\u751f\u7684\u5b9a\u4e49\u4e4b\u5916\uff0c\u968f\u673a\u70ed\u529b\u5b66\u4e2d\u5f15\u5165\u7684\u5176\u4ed6\u70ed\u529b\u5b66\u91cf\u8fd8\u5305\u62ec\u66f4\u52a0\u7ec6\u81f4\u7684 housekeeping \u70ed\u3001exce<\/span>ss \u70ed[33,34]\u3001\u73af\u6d41[32,35,36]\u7b49<\/span>\u6982\u5ff5\u3002\u8fd9\u4e9b\u662f\u8fd1\u4e9b\u5e74Espos<\/span>ito\u7b49[37-39]\u5de5\u4f5c<\/span>\u7684\u57fa\u7840\u3002<\/span><\/section>\n

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3.1 \u7ecf\u5178\u6da8\u843d\u5b9a\u7406<\/strong><\/span><\/section>\n

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\u5bf9\u4e8e\u5c0f\u7cfb\u7edf\u7684\u975e\u5e73\u8861\u8fc7\u7a0b\uff0c\u7269\u7406\u5b66\u5bb6\u4ece1993\u5e74\u5f00\u59cb\u9646\u7eed\u53d1\u73b0\u4e86\u5f88\u591a\u5bf9\u4e8e\u4efb\u610f\u539f\u7406\u5e73\u8861\u8fc7\u7a0b\u90fd\u4e25\u683c\u6210\u7acb\u7684\u6052\u7b49\u5f0f\uff0c\u7edf\u79f0\u4e3a\u6da8\u843d\u5b9a\u7406<\/strong>\u3002<\/span>\u800c<\/span>\u70ed<\/span>\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u4f5c\u4e3a\u63a8\u8bba\u4ece\u6da8\u843d\u5b9a\u7406\u5bfc\u51fa<\/span>\u3002\u6da8\u843d\u5b9a\u7406\u6709\u5f88\u591a\uff0c\u5176\u4e2d\u6700\u8457\u540d\u7684\u7ed3\u679c\u4fbf\u662f Jarzynski \u6052\u7b49\u5f0f<\/span><\/strong>\uff0c\u7531 Jarzynski [28,30]\u4e8e 1<\/span>997 \u5e74\u63d0\u51fa\uff1a<\/span><\/section>\n

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Jarzynski \u6052\u7b49\u5f0f\u6210\u7acb\u7684\u6761\u4ef6\u662f\u521d\u6001\u4e3a\u70ed\u5e73\u8861\u6001\u3002\u5bf9 Jarzynski \u6052\u7b49\u5f0f\u5229\u7528\u4e00\u6b21Jensen\u4e0d\u7b49\u5f0f\u27e8ex<\/sup><\/em>\u27e9\u2a7ee\u27e8x<\/em>\u27e9<\/sup>,\u4fbf\u5f88\u5bb9\u6613\u5f97\u5230(12)\u5f0f\uff0c\u5373\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u3002\u53e6\u5916\u53ef\u4ee5\u770b\u5230\u5728\u5c0f\u7cfb\u7edf\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u4f1a\u6709\u4e00\u5b9a\u7684\u6982\u7387\u88ab\u201c\u8fdd\u53cd\u201d\u3002\u5176\u6982\u7387\u7531\u516c\u5f0fP<\/em>[W<\/em><\u0394F<\/em>\u2212\u03b6<\/em>]\u2a7de\u2212\u03b2\u03b6<\/em><\/sup>\u7ed9<\/span>\u51fa[40]\u3002<\/span>\u5f53\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\u8db3\u591f\u5c11\uff0c\u0394F<\/em>\u548cW<\/em>\u53ea\u6709k<\/em>B<\/sub>T<\/em>\u91cf\u7ea7\u65f6\uff0c\u8fd9\u79cd\u201c\u8fdd\u53cd\u201d\u5177\u6709\u660e\u663e\u7684\u53ef\u89c2\u6d4b\u6548\u5e94\u3002\u4f46\u662f\u968f\u7740\u7cfb\u7edf\u81ea\u7531\u5ea6\u589e\u52a0\uff0c\u8fd9\u79cd\u201c\u8fdd\u53cd\u201d\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u6982\u7387\u5448\u6307\u6570\u7ea7\u964d\u4f4e\uff0c\u5728\u5b8f\u89c2\u7cfb\u7edf\u53d8\u5f97\u4e0d\u53ef\u80fd\u3002Jarzynski \u6052\u7b49\u5f0f\u6700\u5927\u7684\u610f\u4e49\u5728\u4e8e\u5c06\u4e00\u822c\u975e\u5e73\u8861\u8fc7\u7a0b\u4e2d\u70ed\u529b\u5b66\u91cf\u6ee1\u8db3\u7684\u4e0d\u7b49\u5f0f\u5173\u7cfb\u6539\u5199\u6210\u4e86\u6052\u7b49\u5f0f\uff0c\u8fd9\u662f\u975e\u5e73\u8861\u70ed\u529b\u5b66\u9886\u57df\u5177\u6709\u91cc\u7a0b\u7891\u610f\u4e49\u7684\u521b\u65b0<\/strong>\u3002\u53e6\u5916\uff0cJarzynski \u6052\u7b49\u5f0f\u6307\u51fa\uff0c\u5e73\u8861\u6001\u81ea\u7531\u80fd\u5dee\u503c\u53ef\u4ee5\u901a\u8fc7\u4efb\u610f\u975e\u5e73\u8861\u8fc7\u7a0b\u6765\u8fdb\u884c\u6d4b\u91cf\uff0c\u5373\u5e73\u8861\u6001\u7684\u4fe1\u606f\u53ef\u4ee5\u4ece\u975e\u5e73\u8861\u8fc7\u7a0b<\/span>\u5f97\u5230[29]\uff0c<\/span>\u8fd9\u5728\u5206\u5b50\u7684\u81ea\u7531\u80fd\u5b9e\u9a8c\u6d4b\u91cf\u9886\u57df\uff0c\u5c24\u5176\u662f\u7eb3\u7c73\u5c3a\u5ea6\u7684\u5b9e\u9a8c\u4e2d\u5f97\u5230\u4e86\u5e7f\u6cdb<\/span>\u7684\u5e94\u7528[41,42]\u3002\u503c\u5f97<\/span>\u6307\u51fa\u7684\u662f\uff0cJarzynski \u56e0\u4e3a\u4ed6\u7684\u8fd9\u9879\u5f00\u521b\u6027\u7684\u7814\u7a76\uff0c\u88ab\u7f8e\u56fd\u7269\u7406\u5b66\u4f1a\u6388\u4e882019\u5e74\u5ea6 Las Onsager \u5956\u3002\u800c\u7528\u6765\u9a8c\u8bc1 Jarzynski \u6052\u7b49\u5f0f\u7684\u5de5\u5177\u2014\u2014\u5149\u954a\u6280\u672f\u7684\u53d1\u660e\u4eba A. Ashkin \u88ab\u6388\u4e882018\u5e74\u5ea6\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u3002<\/span><\/section>\n

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\u7406\u8bba\u4e0a\uff0cJarzynski \u6052\u7b49\u5f0f\u53ef\u4ee5\u7ecf\u7531\u591a\u79cd\u9014\u5f84\u63a8\u5bfc\u51fa\u6765[30]\u3002\u53e6\u5916\uff0c\u5b83\u7684\u6b63\u786e\u6027\u548c\u666e\u9002\u6027<\/span> (\u4efb\u610f\u7cfb\u7edf\u3001\u4efb\u610f\u6e29\u5ea6\u3001\u4efb\u610f\u901f\u5ea6) <\/span>\u901a\u8fc7\u4e86\u5f88\u591a\u6570\u503c\u6a21\u62df\u7814\u7a76\u7684\u68c0\u9a8c\u548c\u5b9e\u9a8c\u9a8c\u8bc1[30]\u3002\u4f5c\u4e3a\u6700\u65e9\u88ab\u53d1\u73b0\u548c\u81f3\u4eca\u4ec5\u6709\u7684\u51e0\u4e2a\u63cf\u8ff0\u4efb\u610f\u8fdc\u79bb\u5e73\u8861\u8fc7\u7a0b\u7684\u70ed\u529b\u5b66\u6052\u7b49\u5f0f<\/span> (\u53e6\u5916\u8fd8\u6709Crooks\u6da8\u843d\u5b9a\u7406[43]\u7b49) <\/span>\u4e4b\u4e00\uff0c\u5b83\u4e3a\u7814\u7a76\u8fdc\u79bb\u5e73\u8861\u8fc7\u7a0b\u7684\u70ed\u529b\u5b66\u6253\u5f00\u4e86\u4e00\u6247\u7a97\u3002<\/span><\/section>\n

<\/section>\n
Jarzynski \u6052\u7b49\u5f0f\u7684\u53d1\u73b0\u662f\u70ed\u529b\u5b66\u7814\u7a76\u5386\u53f2\u4e0a\u7684\u4e00\u5ea7\u91cc\u7a0b\u7891\u3002\u5b83\u9996\u6b21\u5efa\u7acb\u4e86\u8fdc\u79bb\u5e73\u8861\u8fc7\u7a0b\u7684\u6052\u7b49\u5f0f<\/span><\/strong>\u3002\u5728\u90a3\u4e4b\u540e\u7814\u7a76\u4eba\u5458\u9646\u7eed\u53d1\u73b0\u4e86\u4e00\u4e9b\u6bd4Jarzynski\u6052\u7b49\u5f0f\u66f4\u52a0\u7ec6\u81f4\u7684\u6da8\u843d\u5b9a<\/span>\u7406\uff0c\u6bd4\u5982Crooks\u6da8\u843d\u5b9a\u7406[43]\u3001Hummer-Szabo\u6da8\u843d\u5b9a\u7406[44]\u548c\u5fae\u5206\u6da8\u843d\u5b9a\u7406[45,46]\u3002<\/span>\u8fd9\u4e9b\u6da8\u843d\u5b9a\u7406\u6784\u6210\u4e86\u4e00\u4e2a\u201c\u5bb6\u65cf\u201d\u3002\u6587\u732e[47]\u6574\u7406\u4e86\u8fd9\u4e9b\u6da8\u843d\u5b9a\u7406\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u53c2\u89c1\u56fe7\u3002<\/span><\/section>\n

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\u56fe7 \u6da8\u843d\u5b9a\u7406\u5bb6\u65cf\uff0c\u8fd9\u4e9b\u6da8\u843d\u5b9a\u7406\u5e76\u4e0d\u4e92\u76f8\u7b49\u4ef7\uff0c\u7bad\u5934\u4ee3\u8868\u201c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u201d\uff0c\u8be6\u60c5\u89c1\u6587\u732e[47]<\/span><\/section>\n<\/section>\n
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\u4e0d\u96be\u770b\u51fa\u201c\u5fae\u5206\u6da8\u843d\u5b9a\u7406\u201d\u5728\u6574\u4e2a\u9886\u57df\u5360\u636e\u7740\u7279\u522b\u91cd\u8981\u7684\u5730\u4f4d\u3002\u5176\u4ed6\u6da8\u843d\u5b9a\u7406\u90fd\u53ef\u4ee5\u4ece\u8fd9\u4e2a\u6700\u57fa\u672c\u7684\u6da8\u843d\u5b9a\u7406\u63a8\u5bfc\u51fa\u6765\u3002\u867d\u7136Jarzynski\u6052\u7b49\u5f0f\u7b49\u7c97\u7c92\u5316\u7684\u6da8\u843d\u5b9a\u7406\u65e9\u57282002\u20142005\u5e74\u524d\u540e\u5c31\u5df2\u7ecf\u5728\u591a\u79cd\u5b9e\u9a8c\u7cfb\u7edf\u4e2d<\/span> (\u6bd4\u5982\u5355\u4e2aRNA \u5206\u5b50\u94fe\u548c\u6c34\u6eb6\u6db2\u4e2d\u7684\u80f6\u4f53\u7c92\u5b50) <\/span>\u5f97\u4ee5\u9a8c\u8bc1\uff0c\u4f46\u662f\u201c\u5fae\u5206\u6da8\u843d\u5b9a\u7406\u201d\u7684\u5b9e\u9a8c\u9a8c\u8bc1\u5374\u4e00\u76f4\u662f\u4e00\u9879\u5de8\u5927\u7684\u6311\u6218\uff0c\u56e0\u4e3a\u6d4b\u91cf\u80f6\u4f53\u7c92\u5b50\u7684\u77ac\u65f6\u901f\u5ea6\u5bf9\u5b9e\u9a8c\u6280\u672f\u63d0\u51fa\u4e86\u6781\u9ad8\u7684\u8981\u6c42\u30022017 \u5e74\uff0c\u672c\u6587\u4f5c\u8005\u4e4b\u4e00\u548c\u7f8e\u56fd\u666e\u6e21\u5927\u5b66\u7684\u674e\u7edf\u85cf\u6559\u6388\u7814\u7a76\u7ec4[47]\u5408\u4f5c\uff0c\u501f\u52a9\u4ed6\u4eec\u53d1\u5c55\u51fa\u6765\u7684\u8d85\u9ad8\u65f6\u7a7a\u5206\u8fa8\u7684\u5149\u529b\u7cfb\u7edf\u5b9e\u9a8c\u5e73\u53f0\uff0c\u6d4b\u91cf\u4e86\u675f\u7f1a\u5728\u7a7a\u6c14\u4e2d\u7684\u7eb3\u7c73\u5c0f\u7403\u5728\u6fc0\u5149\u9a71\u52a8\u65f6\u4f4d\u7f6e\u548c\u77ac\u65f6\u901f\u5ea6\u968f\u65f6\u95f4\u7684\u6f14\u5316\u3002\u901a\u8fc7\u83b7\u53d6\u5927\u91cf\u8f68\u9053\u6570\u636e\uff0c\u7b2c\u4e00\u6b21\u5728\u5b9e\u9a8c\u4e0a\u9a8c\u8bc1\u4e86\u8fd9\u4e2a\u88ab\u79f0\u4e3a\u6da8\u843d\u5b9a\u7406\u4e4b\u6bcd\u7684\u201c\u5fae\u5206\u6da8\u843d\u5b9a\u7406\u201d\u3002\u8fd9\u9879\u5de5\u4f5c\u5c06\u968f\u673a\u70ed\u529b\u5b66\u5b9e\u9a8c\u7814\u7a76\u4ece\u8fc7\u963b\u5c3c\u60c5\u5f62\u62d3\u5c55\u5230\u4e86\u6b20\u963b\u5c3c\u60c5\u5f62\uff0c\u5e76\u4e14\u628a\u8fd9\u4e2a\u6700\u57fa\u672c\u7684\u6da8\u843d\u5b9a\u7406\u4e43\u81f3\u6240\u6709\u5176\u4ed6\u7684\u6709\u5173\u975e\u5e73\u8861\u529f\u7684\u6da8\u843d\u5b9a\u7406\u90fd\u5efa\u7acb\u5728\u4e86\u575a\u5b9e\u7684\u5b9e\u9a8c\u57fa\u7840\u4e4b\u4e0a\u3002<\/span><\/section>\n

<\/section>\n
\u503c\u5f97\u6307\u51fa\u7684\u662f\uff0c\u5728\u8fd9\u4e9b\u6da8\u843d\u5b9a\u7406\u4e2d\uff0c\u8d8a\u7c97\u7c92\u5316\u7684\u53d1\u73b0\u5f97\u8d8a\u65e9\uff0c\u8d8a\u7cbe\u7c92\u5316\u7684\u53d1\u73b0\u5f97\u8d8a\u665a\u3002\u8003\u8651\u5230\u6da8\u843d\u5b9a\u7406\u662f\u5bf9\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u4e0d\u540c\u5f62\u5f0f\u7684\u63a8\u5e7f\uff0c\u4e0d\u96be\u5f97\u5230\u5982\u4e0b\u7ed3\u8bba\uff1a\u7269\u7406\u5b66\u5bb6\u5bf9\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u8ba4\u8bc6\u4e5f\u662f\u5faa\u5e8f\u6e10\u8fdb\uff0c\u9010\u6b65\u6df1\u5165\u7684\u3002\u8fd9\u4e00\u70b9\u4e0e\u7269\u7406\u5b66\u5bb6\u5bf9\u539f\u5b50\u7ed3\u6784\u7684\u8ba4\u8bc6\u8fc7\u7a0b\u975e\u5e38\u76f8\u4f3c\u3002<\/span><\/section>\n

<\/section>\n
\u9664\u4e86\u4e0e\u529f\u6709\u5173\u7684\u6da8\u843d\u5b9a\u7406\uff0c\u8fd8\u6709\u4e00\u4e2a\u6709\u5173\u70ed\u4ea4\u6362\u7684\u6da8\u843d<\/span>\u5b9a\u7406[48]\uff0c<\/span>\u5b83\u63cf\u8ff0\u7684\u662f\u4e00\u4e2a\u521d\u59cb\u65f6\u5904\u4e8e\u6e29\u5ea6\u03b2<\/em>s<\/sub>\u7684\u7cfb\u7edf\u8ddf\u4e00\u4e2a\u5904\u4e8e\u6e29\u5ea6\u03b2<\/em>\u7684\u70ed\u5e93\u5728\u63a5\u89e6\u8fc7\u7a0b\u4e2d\u70ed\u4ea4\u6362\u6ee1\u8db3\u5982\u4e0b\u7684\u6052\u7b49<\/span>\u5f0f[48]<\/span>\uff1a<\/span><\/section>\n

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\u5176\u4e2dQ<\/em>\u662f\u7cfb\u7edf\u4ece\u70ed\u5e93\u5438\u70ed\u3002\u5229\u7528Jensen\u4e0d\u7b49\u5f0f\uff0c\u53ef\u4ee5\u5f97\u5230<\/span><\/section>\n

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(15)\u5f0f\u4e3aClausius\u4e0d\u7b49\u5f0f\uff0c\u53ea\u80fd\u4ece\u76f8\u5bf9\u7684\u9ad8\u6e29\u70ed\u6e90\u5438\u6536\u70ed\u91cf\u3002\u5982\u679c\u628a\u6709\u5173\u505a\u529f\u548c\u70ed\u4ea4\u6362\u7684\u6da8\u843d\u5b9a\u7406\u5408\u5e76\u8d77\u6765\u8003\u8651\uff0c\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u591a\u70ed\u5e93\u65f6\u7684\uff0c\u5173\u4e8e\u529f\u548c\u70ed\u7684\u8054\u5408\u5206\u5e03\u7684\u6da8\u843d\u5b9a<\/span>\u7406[49]<\/span>\uff1a<\/span><\/section>\n

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\u4ee5\u4e0a\u5173\u4e8e\u529f\u548c\u70ed\u7684\u6da8\u843d\u5b9a\u7406\u90fd\u662f\u5728\u7ec6\u81f4\u5e73\u8861\u6761\u4ef6\u6210\u7acb\u65f6\u7684\u7ed3\u679c\u3002\u5f53\u7ec6\u81f4\u5e73\u8861\u6761\u4ef6\u4e0d\u6210\u7acb\u65f6\uff0c\u8fd8\u6709\u5176\u4ed6\u4e00\u4e9b\u6da8\u843d\u5b9a\u7406\uff1a\u6bd4\u8f83\u77e5\u540d\u7684\u6709Evans-Searles\u6da8\u843d<\/span>\u5b9a\u7406[50,51]\u548c<\/span>Gallavotti-Cohen\u6da8\u843d<\/span>\u5b9a\u7406[52,53]\u3002\u4ece\u8fd9\u4e9b\u7ec6\u81f4\u5e73\u8861\u6761\u4ef6\u88ab\u7834\u574f\u7684\u6da8\u843d\u5b9a\u7406\u51fa\u53d1\uff0c\u8fd8\u53ef\u4ee5\u63a8\u5bfc\u51fa\u6240\u8c13\u7684\u70ed\u529b\u5b66\u4e0d\u786e\u5b9a\u6027\u5173\u7cfb[54,55]\u3002<\/span>\u7531\u4e8e\u7bc7\u5e45\u6240\u9650\uff0c\u5bf9\u8fd9\u4e9b\u5185\u5bb9\u4e0d\u518d\u8be6\u8ff0\u3002<\/span><\/section>\n

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3.2 \u91cf\u5b50\u6da8\u843d\u5b9a\u7406<\/strong><\/span><\/section>\n

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\u7814\u7a76\u4eba\u5458\u6700\u521d\u5bf9\u6709\u5173\u968f\u673a\u70ed\u529b\u5b66\u548c\u6da8\u843d\u5b9a\u7406\u7684\u7814\u7a76\u4e3b\u8981\u805a\u7126\u4e8e\u7ecf\u5178\u7cfb\u7edf\uff0c\u6b64\u540e\u5f00\u59cb\u601d\u8003\u5c06\u70ed\u529b\u5b66\u7684\u7406\u8bba\u6846\u67b6\u548c\u6da8\u843d\u5b9a\u7406\u63a8\u5e7f\u5230\u91cf\u5b50\u7cfb\u7edf\u3002\u5411\u91cf\u5b50\u529b\u5b66\u7684\u63a8\u5e7f\u5e76\u4e0d\u662f\u975e\u5e38\u76f4\u63a5\u7684\uff0c\u56e0\u4e3a\u91cf\u5b50\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001\u7528Hilbert\u7a7a\u95f4\u7684\u77e2\u91cf\u8868\u793a\uff0c\u800c\u7ecf\u5178\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001\u7528\u76f8\u7a7a\u95f4\u7684\u4e00\u4e2a\u70b9\u4ee3\u8868\u3002\u53e6\u5916\uff0c\u91cf\u5b50\u7cfb\u7edf\u91cc\u7684\u6d4b\u91cf\u3001\u6ce2\u51fd\u6570\u584c\u7f29\u3001\u91cf\u5b50\u8f68\u9053\u7b49\u6982\u5ff5\u4e0e\u7ecf\u5178\u7cfb\u7edf\u5177\u6709\u660e\u663e\u7684\u533a\u522b\u3002\u7ecf\u5178\u7c92\u5b50\u5728\u76f8\u7a7a\u95f4\u6709\u5f88\u597d\u5b9a\u4e49\u7684\u8f68\u9053\uff0c\u4ece\u800c\u53ef\u4ee5\u5b9a\u4e49\u8f68\u9053\u529f\u3001\u8f68\u9053\u70ed\u7b49\u6982\u5ff5\uff0c\u4f46\u7531\u4e8e\u91cf\u5b50\u4e0d\u786e\u5b9a\u6027\u539f\u7406\uff0c\u5bf9\u91cf\u5b50\u7cfb\u7edf\u4e0d\u80fd\u5f88\u597d\u5730\u5b9a\u4e49\u8f68\u9053\u3002\u8fd9\u4e9b\u533a\u522b\u7ed9\u91cf\u5b50\u968f\u673a\u70ed\u529b\u5b66\u548c\u91cf\u5b50\u6da8\u843d\u5b9a\u7406\u7684\u7814\u7a76\u5e26\u6765\u4e86\u6311\u6218\u3002\u4e0b\u9762\u7b80\u8981\u4ecb\u7ecd\u628a\u968f\u673a\u70ed\u529b\u5b66\u548c\u6da8\u843d\u5b9a\u7406\u5411\u91cf\u5b50\u7cfb\u7edf\u7684\u63a8\u5e7f\u3002<\/span><\/section>\n

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\u91cf\u5b50\u5b64\u7acb\u7cfb\u7edf\u662f\u6307\u5728\u9a71\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u7cfb\u7edf\u4e0d\u4e0e\u5916\u754c\u70ed\u5e93\u53d1\u751f\u76f8\u4e92\u4f5c\u7528\uff0c\u6240\u4ee5\u6ca1\u6709\u70ed\u4ea4\u6362\u3002\u5728\u91cf\u5b50\u5b64\u7acb\u7cfb\u7edf\u4e2d\uff0c\u7cfb\u7edf\u7684\u5e7a\u6b63\u6f14\u5316\u7b97\u7b26\u4e3a<\/span><\/section>\n

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\n
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\n

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\u5176\u4e2dT<\/em>\u662f\u7f16\u65f6\u7b97\u7b26\u3002\u5728\u6574\u4e2a\u9a71\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u5916\u754c\u5bf9\u7cfb\u7edf\u4f1a\u505a\u529fW<\/em>\u3002\u7531\u4e8e\u662f\u91cf\u5b50\u5b64\u7acb\u7cfb\u7edf\uff0c\u8fc7\u7a0b\u4e2d\u5e76\u6ca1\u6709\u4e0e\u70ed\u5e93\u7684\u70ed\u4ea4\u6362\uff0c\u90a3\u4e48\u505a\u529f\u503c\u4fbf\u662f\u6f14\u5316\u524d\u540e\u7684\u80fd\u91cf\u5dee\u3002\u6807\u51c6\u7684\u91cf\u5b50\u529f\u7684\u5b9a\u4e49\u662f\u57fa\u4e8e\u4e24\u6b21\u80fd\u91cf\u6295\u5f71\u6d4b\u91cf<\/span> (two-projective energy measurement\uff0cTPM)<\/span> W <\/em>:=En<\/sub>\u03c4<\/sup><\/em>\u2212Em<\/sub><\/em>0<\/sup>\uff0c2000\u5e74\u7531Kurchan[56]\u548c Tasaki[57]\u5206\u522b\u72ec\u7acb\u63d0\u51fa\u3002\u5373\u5728\u521d\u59cb\u65f6\u523b\u65f6\u5148\u505a\u4e00\u6b21\u80fd\u91cf\u6295\u5f71\u6d4b\u91cf\uff0c\u8b6c\u5982\u7cfb\u7edf\u7684\u6001\u584c\u7f29\u5230\u4e86\u521d\u6001\u54c8\u5bc6\u987f\u91cf<\/span>\u7684\u7b2cm<\/em>\u4e2a\u80fd\u91cf\u672c\u5f81\u6001\uff0c\u7136\u540e\u4ece\u8fd9\u4e2a\u80fd\u91cf\u672c\u5f81\u6001\u5f00\u59cb\u6f14\u5316\uff0c\u5728\u7ec8\u6b62\u65f6\u523b\u65f6\u518d\u8fdb\u884c\u4e00\u6b21\u80fd\u91cf\u6295\u5f71\u6d4b\u91cf\uff0c\u8fd9\u65f6\u7cfb\u7edf\u7684\u6001\u53ef\u80fd\u584c\u7f29\u5230\u4e86\u672b\u6001\u54c8\u5bc6\u987f\u91cf<\/span>\u7684\u7b2cn<\/em>\u4e2a\u80fd\u91cf\u672c\u5f81\u6001\uff0c\u6574\u4e2a\u8fc7\u7a0b\u79f0\u4e3a\u4e00\u6b21\u5b9e\u9a8c\u3002\u5728\u8fd9\u6b21\u5b9e\u9a8c\u4e2d\uff0c\u80fd\u91cf\u5deeW<\/em>\u4fbf\u88ab\u5b9a\u4e49\u4e3a\u91cf\u5b50\u529f\u3002\u5f53\u7136\u53ef\u4ee5\u91cd\u590d\u5f88\u591a\u6b21\u5b9e\u9a8c\uff0c\u6bcf\u6b21\u5f97\u5230\u7684\u529f\u7684\u503c\u90fd\u53ef\u80fd\u4e0d\u4e00\u6837\uff0c\u6700\u540e\u4fbf\u6709\u4e00\u4e2a\u529f\u5206\u5e03P<\/em>(W<\/em>)\u3002\u6574\u4e2a\u8fc7\u7a0b\u7684\u793a\u610f\u56fe\u89c1\u56fe8\u3002<\/span><\/section>\n<\/section>\n
\n
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\n
\u56fe8 \u57fa\u4e8e\u4e24\u6b21\u6295\u5f71\u5b9a\u4e49\u7684\u8f68\u9053\u529f\u3002\u8fd9\u91cc\u663e\u793a\u4e86\u4e00\u6b21\u5b9e\u9a8c\u7684\u7ed3\u679c\uff0c\u4ece\u7b2c2\u4e2a\u672c\u5f81\u6001\u8df3\u5230\u7b2c4\u4e2a\u77ac\u65f6\u672c\u5f81\u6001<\/span><\/section>\n<\/section>\n
\n

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\u529f\u5206\u5e03\u4e0d\u4ec5\u4e0e\u521d\u6001\u7684\u6982\u7387\u5206\u5e03pm<\/sub><\/em>0<\/sup>\u6709\u5173\uff0c\u8fd8\u4e0e\u8dc3\u8fc1\u77e9\u9635\u5143P<\/em>m<\/sub><\/em>,n<\/em><\/sub>\u6709\u5173\uff1a<\/span><\/section>\n

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\n
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\n

<\/span><\/section>\n
\u5f0f\u4e2dpm<\/sub><\/em>0<\/sup><\/sub>\u4e3a\u7b2c\u4e00\u6b21\u6d4b\u91cf\u5f97\u5230\u7b2cm<\/em>\u4e2a\u672c\u5f81\u6001\u7684\u6982\u7387\uff0c\u5373\u4e3a<\/span>\u7684\u7b2cm<\/em>\u4e2a\u5bf9\u89d2\u5143\u3002P<\/em>m<\/sub><\/em>,n<\/em><\/sub>\u4e3a\u8dc3\u8fc1\u77e9\u9635\u5143\uff0c\u8868\u793a\u4ece\u521d\u59cb\u65f6\u523b\u7684\u7b2cm<\/em>\u4e2a\u672c\u5f81\u6001\u8dc3\u8fc1\u5230\u7ec8\u6b62\u65f6\u523b\u7684\u7b2cn<\/em>\u4e2a\u672c\u5f81\u6001\u7684\u6982\u7387\uff1a<\/span><\/section>\n

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\n
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\n

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\u57fa\u4e8e TPM \u7684\u91cf\u5b50\u529f\u7684\u5b9a\u4e49\u6700\u5927\u7684\u597d\u5904\u662f\u6ee1\u8db3\u91cf\u5b50 Jarzynski\u6052\u7b49<\/span>\u5f0f[56-58]<\/span>\uff0c\u5f62\u5f0f\u4e0e\u7ecf\u5178\u60c5\u5f62\u4e0b\u7684 Jarzynski \u6052\u7b49\u5f0f(13)\u5f0f\u5b8c\u5168\u4e00\u81f4\uff0c\u6210\u7acb\u6761\u4ef6\u4ecd\u9700\u8981\u521d\u6001\u4e3a\u70ed\u5e73\u8861\u6001\uff1a<\/span>,\u5176\u4e2dZ<\/em>0<\/sub>\u4e3a\u521d\u59cb\u65f6\u523b\u7684\u914d\u5206\u51fd\u6570<\/span>\u3002\u91cf\u5b50Jarzynski\u6052\u7b49\u5f0f\u7684\u7b80\u5355\u8bc1\u660e\u5982<\/span>\u4e0b[56,57]<\/span>\uff1a<\/span><\/section>\n

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\n
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\n

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\u5176\u4e2d\u7528\u5230\u4e86\u5e7a\u6b63\u6f14\u5316\u7b97\u7b26<\/span>\u7684\u5e7a\u6b63\u6027\u8d28\u3002<\/span><\/section>\n

<\/section>\n
2013\u5e74\u4e24\u4e2a\u7814\u7a76<\/span>\u7ec4[59,60]\u63d0\u51fa\u95f4\u63a5\u9a8c\u8bc1\u91cf\u5b50Jarzynski\u6052\u7b49\u5f0f\u7684\u65b9\u6848\u2014\u2014\u5c06\u529f\u5206\u5e03\u7684\u5085\u91cc\u53f6\u53d8\u6362\u6620\u5c04\u4e3a\u4e00\u4e2a\u91cf\u5b50\u5f00\u653e\u7cfb\u7edf\u7684\u9000\u76f8\u5e72\u56e0\u5b50\u3002\u901a\u8fc7\u6d4b\u91cf\u8fd9\u4e2a\u9000\u76f8\u5e72\u56e0\u5b50\u95f4\u63a5\u83b7\u5f97\u529f\u5206\u5e03\u7684\u4fe1\u606f\u3002\u8fd9\u4e2a\u65b9\u6848\u6700\u7ec8\u57282014\u5e74\u88ab\u5b9e\u9a8c\u9a8c\u8bc1[61]\u3002\u91cf\u5b50Jarzynski\u6052\u7b49\u5f0f\u7684\u76f4\u63a5\u5b9e\u9a8c\u9a8c\u8bc1\u7531\u672c\u6587\u4f5c\u8005\u4e4b\u4e00\u4e0e\u6e05\u534e\u5927\u5b66\u91d1\u5947\u5942\u6559\u6388[62]\u5408\u4f5c<\/span>\u5b8c\u6210\u3002\u901a\u8fc7\u53d1\u5c55\u4e00\u79cd\u9002\u7528\u4e8e\u5355\u79bb\u5b50\u7684\u58f0\u5b50\u6295\u5f71\u6d4b\u91cf\u6280\u672f\uff0c\u6700\u7ec8\u5b9e\u73b0\u4e86\u5bf9\u91cf\u5b50\u529b\u5b66\u7cfb\u7edf\u505a\u529f\u7684\u6d4b\u91cf\uff0c\u5e76\u6210\u529f\u9a8c\u8bc1\u4e86\u91cf\u5b50Jarzynski\u6052\u7b49\u5f0f\u3002\u8fd9\u4e2a\u5de5\u4f5c\u5728\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u9886\u57df\u4ea7\u751f\u4e86\u4e00\u5b9a\u7684\u56fd\u9645\u5f71\u54cd\u3002<\/span><\/section>\n

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\u5728\u7ecf\u5178\u529b\u5b66\u548c\u7ecf\u5178\u70ed\u529b\u5b66\u4e2d\uff0c\u529f\u7684\u5b9a\u4e49\u975e\u5e38\u6e05\u695a\uff0c\u4f46\u76f8\u5e94\u7684\u91cf\u5b50\u529b\u5b66\u7684\u505a\u529f\u4e00\u76f4\u56f0\u6270\u7740\u7269\u7406\u5b66\u5bb6\u30022000\u5e74\uff0cJarzynski\u521a\u63d0\u51fa\u4ed6\u7684\u6052\u7b49\u5f0f\u4e0d\u4e45\uff0c\u6cd5\u56fd\u7269\u7406\u5b66\u5bb6Kurcha<\/span>n[56]\u548c\u65e5<\/span>\u672c\u7269\u7406\u5b66\u5bb6Tasa<\/span>ki[57]\u5c31\u5f88<\/span>\u5feb\u5c06Jarzynski\u6052\u7b49\u5f0f\u63a8\u5e7f\u5230\u4e86\u91cf\u5b50\u529b\u5b66\u7cfb\u7edf\u3002\u4e0d\u8fc7\uff0c\u4ed6\u4eec\u4e3a\u4e86\u5f97\u5230\u8fd9\u4e2a\u91cf\u5b50Jarzynski\u6052\u7b49\u5f0f\uff0c\u5f15\u5165\u4e86\u4e00\u4e2a\u975e\u5e38\u53cd\u76f4\u89c2\u7684\u57fa\u4e8e\u4e24\u6b21\u6295\u5f71\u5b9a\u4e49\u7684\u91cf\u5b50\u8f68\u9053\u529f\u7684\u6982\u5ff5\uff0c\u800c\u91cf\u5b50\u6295\u5f71\u610f\u5473\u7740\u6ce2\u5305\u584c\u7f29\u5047\u8bbe\uff0c\u8fd9\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\u662f\u6709\u4e89\u8bae\u7684\u3002\u4ece2000-2015\u5e74\uff0c\u91cf\u5b50\u8f68\u9053\u529f\u7684\u5b9a\u4e49\u548c\u5185\u6db5\u4e00\u76f4\u662f\u7814\u7a76\u7684\u7126\u70b9\uff0c\u4f46\u51e0\u4e4e\u6ca1\u6709\u4efb\u4f55\u8fdb\u5c55\u3002<\/span><\/section>\n

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2015\u5e74\uff0c\u672c\u6587\u4f5c\u8005\u4e4b\u4e00\u548c\u5408\u4f5c\u8005[63]\u5bf9\u8fd9\u4e2a\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u7684\u91cd\u8981\u95ee\u9898\u2014\u2014\u91cf\u5b50\u529b\u5b66\u8f68\u9053\u529f\u7684\u5b9a\u4e49\u548c\u5185\u6db5\u8fdb\u884c\u4e86\u6df1\u5165\u7814\u7a76\uff0c\u5229\u7528\u534a\u7ecf\u5178\u529b\u5b66\u7684\u529e\u6cd5\uff0c\u7b2c\u4e00\u6b21\u4e25\u683c\u89e3\u6790\u8bc1\u660e\u4e86\u91cf\u5b50\u8f68\u9053\u529f\u6ee1\u8db3\u91cf\u5b50\u529b\u5b66\u201c\u5bf9\u5e94\u539f\u7406\u201d\uff0c\u5e76\u7b2c\u4e00\u6b21\u63ed\u793a\u4e86\u91cf\u5b50\u529b\u5b66\u7684\u8f68\u9053\u529f\u548c\u7ecf\u5178\u529b\u5b66\u7684\u8f68\u9053\u529f\u7684\u8054\u7cfb\u3002\u8fd9\u4e3a\u57fa\u4e8e\u4e24\u6b21\u6295\u5f71\u65b9\u6cd5\u5b9a\u4e49\u7684\u91cf\u5b50\u8f68\u9053\u529f\u627e\u5230\u4e86\u4e00\u4e2a\u4f50\u8bc1\uff0c\u4ece\u800c\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u8bc1\u660e\u4e86\u57fa\u4e8e\u4e24\u6b21\u6295\u5f71\u5b9a\u4e49\u7684\u91cf\u5b50\u8f68\u9053\u529f\u7684\u5408\u7406\u6027\u30022018\u5e74\u672c\u6587\u4f5c\u8005\u4e4b\u4e00\u548c\u5408\u4f5c\u8005Ken Funo[64]\u53c8\u8fdb\u4e00\u6b65\u628a\u4e0a\u8ff0\u5de5\u4f5c\u5411\u524d\u63a8\u8fdb\u3002\u9996\u6b21\u5c06\u8def\u5f84\u79ef\u5206\u65b9\u6cd5\u5f15\u5165\u5230\u91cf\u5b50\u5f00\u7cfb\u7edf\u7684\u70ed\u529b\u5b66\u7814\u7a76\u4e2d\u3002\u5177\u4f53\u8bf4\u6765\uff0c\u8be5\u9879\u7814\u7a76\u5f15\u5165\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u529e\u6cd5<\/span> (\u5b9a\u4e49\u5355\u6761\u8d39\u66fc\u8def\u5f84\u4e0a\u7684\u8f68\u9053\u529f)<\/span>\uff0c\u4ece\u800c\u53ef\u4ee5\u66f4\u597d\u5730\u9610\u660e\u91cf\u5b50\u8f68\u9053\u529f\u548c\u7ecf\u5178\u8f68\u9053\u529f\u4e4b\u95f4\u6df1\u523b\u7684\u5185\u5728\u8054\u7cfb\uff0c\u800c\u4e14\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u628a\u529f\u5206\u5e03\u7684\u5bf9\u5e94\u539f\u7406\u4ece\u539f\u6765\u7684\u5b64\u7acb\u7cfb\u7edf\u63a8\u5e7f\u5230\u91cf\u5b50\u5f00\u653e\u7cfb\u7edf\u3002<\/span><\/section>\n

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\u5728\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u4e2d\uff0c\u7edf\u8ba1\u914d\u5206\u51fd\u6570\u5305\u542b\u4e86\u70ed\u5e73\u8861\u6001\u7684\u91cd\u8981\u4fe1\u606f\u3002\u56e0\u6b64\u53d1\u5c55\u5404\u79cd\u89e3\u6790\u548c\u6570\u503c\u65b9\u6cd5\u8ba1\u7b97\u4e00\u4e2a\u7269\u7406\u7cfb\u7edf\u7684\u914d\u5206\u51fd\u6570\u6210\u4e3a\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u7814\u7a76\u7684\u91cd\u8981\u5185\u5bb9\u3002\u4e0e\u4e4b\u7c7b\u4f3c\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u975e\u5e73\u8861\u9a71\u52a8\u8fc7\u7a0b\uff0c\u5b83\u7684\u529f\u5206\u5e03\u51fd\u6570\u548c\u70ed\u5206\u5e03\u51fd\u6570\u5305\u542b\u4e86\u6709\u5173\u975e\u5e73\u8861\u8fc7\u7a0b\u7684\u91cd\u8981\u4fe1\u606f\u3002\u53d1\u5c55\u5404\u79cd\u65b9\u6cd5\u8ba1\u7b97\u975e\u5e73\u8861\u8fc7\u7a0b\u7684\u529f\u5206\u5e03\u548c\u70ed\u5206\u5e03\u51fd\u6570\u79f0\u4e3a\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u7814\u7a76\u7684\u91cd\u8981\u5185\u5bb9\u3002\u7b14\u8005\u56e2\u961f\u5728\u8fd9\u4e2a\u65b9\u9762\u4e5f\u8fdb\u884c\u4e86\u4e00\u4e9b\u63a2\u7d22\u3002\u6211\u4eec\u8ba1\u7b97\u4e86\u6d3b\u585e\u4e2d\u5355\u4e2a\u5e03\u6717\u7c92\u5b50\u5728\u7b49\u6e29\u8fc7\u7a0b\u7684\u529f\u5206<\/span>\u5e03[65]\uff0c<\/span>\u8154\u91cf\u5b50\u7535\u52a8\u529b\u5b66\u7cfb<\/span>\u7edf[66]\u53ca<\/span>\u6709\u76f8\u4e92\u4f5c\u7528\u7684\u91cf\u5b50\u591a\u4f53\u7cfb<\/span>\u7edf[67]\u5728\u7edd\u70ed\u8fc7\u7a0b\u7684\u529f\u5206\u5e03\u3002\u6b64\u5916\uff0c\u8fd8\u7528\u8def\u5f84\u79ef\u5206\u65b9\u6cd5\u7814\u7a76\u4e86\u91cf\u5b50\u5f00\u7cfb\u7edf\u7684\u8f68\u9053\u70ed\u6ee1\u8db3\u7684\u6da8\u843d\u5b9a\u7406[68,69]\uff0c\u4ee5\u53ca\u5177\u6709\u5bf9\u5076\u5173\u7cfb\u7684\u4e00\u7ef4\u73bb\u8272\u7cfb\u7edf\u4e0e\u4e00\u7ef4\u8d39\u7c73\u7cfb\u7edf\u7684\u505a\u529f\u7684\u5168\u540c\u6027[70]\uff0c\u8fd9\u79cd\u5bf9\u5076\u6027\u4e5f\u4f1a\u4f53\u73b0\u5728\u4ee5\u8fd9\u4e9b\u91cf\u5b50\u591a\u4f53\u4f5c\u4e3a\u5de5\u4f5c\u7269\u8d28\u7684\u91cf\u5b50\u70ed\u673a\u7684\u6548\u7387[71]\u3002\u8fd9\u4e9b<\/span>\u7814\u7a76\u663e\u8457\u62d3\u5c55\u4e86\u5bf9\u91cf\u5b50\u7cfb\u7edf\u505a\u529f\u7684\u7406\u89e3\u3002<\/span><\/section>\n<\/section>\n

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4. \u7edf\u8ba1\u70ed\u529b\u5b66\u5e7f\u4e49\u6b63\u5219\u70ed\u5316\u7406\u8bba\u4e0e\u9ed1\u6d1e\u4fe1\u606f\u4f6f\u8c2c<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u8fd1\u4e9b\u5e74\u6765\uff0c\u91cf\u5b50\u4fe1\u606f\u7684\u53d1\u5c55\u4f7f\u5f97\u4eba\u4eec\u5bf9\u91cf\u5b50\u7ea0\u7f20\u6709\u4e86\u66f4\u52a0\u6df1\u5165\u7684\u7406\u89e3\uff0c\u4ece\u65b0\u7684\u89d2\u5ea6\u5f00\u5c55\u4e86\u7edf\u8ba1\u7269\u7406\u7406\u8bba\u57fa\u7840\u7684\u521b\u65b0\u7814\u7a76\u3002\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u4e00\u4e2a\u57fa\u672c\u5047\u8bbe\u662f\u7b49\u6982\u7387\u5047\u8bbe\uff0c\u5e76\u7531\u6b64\u53d1\u5c55\u51fa\u57fa\u4e8e\u5fae\u6b63\u5219\u7cfb\u7efc\u3001\u6b63\u5219\u7cfb\u7efc\u4ee5\u53ca\u5de8\u6b63\u5219\u7cfb\u7efc\u7684\u7edf\u8ba1\u70ed\u529b\u5b66\u7406\u8bba\u3002\u901a\u5e38\u7684\u6559\u79d1\u4e66\u4ece\u70ed\u5e93\u52a0\u7cfb\u7edf\u6784\u6210\u7684\u5fae\u6b63\u5219\u7cfb\u7efc\u5047\u8bbe\u51fa\u53d1\uff0c\u63a8\u5bfc\u51fa\u7cfb\u7edf\u7684\u6b63\u5219\u7cfb\u7efc<\/span> (\u5409\u5e03\u65af) <\/span>\u5206\u5e03\u3002\u8fd1\u4e9b\u5e74\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u8868\u660e\uff0c\u53ef\u4ee5\u4e0d\u57fa\u4e8e\u4e0a\u8ff0\u7b49\u6982\u7387\u57fa\u672c\u5047\u8bbe\uff0c\u800c\u76f4\u63a5\u5229\u7528\u91cf\u5b50\u7ea0\u7f20\u7684\u89c2\u5ff5\uff0c\u5efa\u7acb\u6b63\u5219\u7cfb\u7efc<\/span> (\u5409\u5e03\u65af) <\/span>\u5206\u5e03[72-74]\u3002<\/span><\/section>\n

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\u7cfb\u7edf\u7684\u72b6\u6001\u53ef\u4ee5\u901a\u8fc7\u6574\u4f53\u80fd\u58f3\u4e0a\u7eaf\u6001|\u03c8<\/em>\u27e9=\u2211Cn<\/sub><\/em>,<\/sub>{nj<\/em>}<\/sub>|n<\/em>,{nj<\/sub><\/em>}\u27e9\u7ea6\u5316\u6389\u73af\u5883\u81ea\u7531\u5ea6\u5f97\u5230\uff0c\u5373\u03c1<\/em>S<\/sub>=TrB<\/sub>[|\u03c8<\/em>\u27e9\u27e8\u03c8<\/em>|]=\u2211P<\/em>n<\/sub><\/em>|n<\/em>\u27e9\u27e8m<\/em>|+\u2211Fnm<\/sub><\/em>|n<\/em>\u27e9\u27e8m<\/em>|\u3002\u53ef\u4ee5\u8bc1\u660eF<\/em>nm<\/em><\/sub>\u5177\u6709\u56e0\u5b50\u5316\u7ed3\u6784\uff0c\u5e76\u4e14\u5728\u73af\u5883\u81ea\u7531\u5ea6\u8db3\u591f\u5927\u7684\u65f6\u5019\u8d8b\u8fd1\u4e8e\u96f6\uff0c\u5373F<\/em>nm<\/em><\/sub>\u21920\u3002\u6839\u636e\u6982\u7387\u8bba\u4e2d\u7684\u5927\u6570\u5b9a\u5f8b\uff0c\u53ef\u4ee5\u8bc1\u660e\u5bf9\u89d2\u9879P<\/em>n<\/sub><\/em>=\u2211\u2223Cn<\/sub><\/em>,<\/sub>{nj<\/em>}<\/sub>\u22232<\/sup>\u7684\u5e73\u5747\u503c\u4e3aP<\/em>n<\/sub><\/em>=\u03a9<\/em>(E<\/em>\u2212\u03b5n<\/sub><\/em>,\u03b4<\/em>)\/\u03a9<\/em>(E<\/em>,\u03b4<\/em>)\uff0c\u5176\u4e2d\u03a9<\/em>(E<\/em>\u2212\u03b5n<\/sub><\/em>,\u03b4<\/em>)\u662f\u73af\u5883\u5728\u80fd\u58f3[E<\/em>\u2212\u03b5n<\/sub><\/em>,E<\/em>\u2212\u03b5n<\/sub><\/em>+\u03b4<\/em>]\u4e0a\u7684\u72b6\u6001\u6570\u3002\u5bf9\u4e8e\u8c10\u632f\u5b50\u73af\u5883\uff0c\u53ef\u4ee5\u5f97\u5230<\/span><\/section>\n

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\u4e0a\u8ff0\u6a21\u578b\u8bf4\u660e\uff0c\u5728\u7cfb\u7edf\u52a0\u73af\u5883\u7684\u6ce2\u51fd\u6570\u96c6\u5408\u4e2d\uff0c\u7edd\u5927\u591a\u6570\u7eaf\u6001\u6ce2\u51fd\u6570\u7ed9\u51fa\u7684\u7cfb\u7edf\u7ea6\u5316\u5bc6\u5ea6\u77e9\u9635\u5728\u70ed\u529b\u5b66\u6781\u9650\u4e0b\u90fd\u6ee1\u8db3\u6b63\u5219\u5206\u5e03\u3002\u5176\u5b9e\uff0c\u5bf9\u4e8e\u5b87\u5b99\u4e2d\u4e00\u4e2a\u8db3\u591f\u5c0f\u7684\u5b50\u7cfb\u7edf\uff0c\u5f53\u6574\u4e2a\u5b87\u5b99\u5904\u4e8e\u4efb\u610f\u4e00\u4e2a\u7eaf\u6001\u65f6<\/span> (\u4e0d\u5fc5\u662f\u7b49\u6982\u7387\u5206\u5e03\u7684\u6df7\u6001)<\/span>\uff0c\u8fd9\u4e2a\u5b50\u7cfb\u7edf\u51e0\u4e4e\u90fd\u8fd1\u4f3c\u5730\u5904\u4e8e\u70ed\u5e73\u8861\u6001\u3002\u8fd9\u79cd\u73b0\u8c61\u88ab\u79f0\u4e3a\u201c\u5e7f\u4e49\u6b63\u5219\u539f\u7406\u201d<\/span> (general canonical principle) <\/span>\u6216\u201c\u6b63\u5219\u5178\u578b\u6027\u201d<\/span> (canonical typicality)<\/span>\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u5c06\u91cf\u5b50\u7edf\u8ba1\u529b\u5b66\u5b8c\u5168\u5efa\u7acb\u5728\u91cf\u5b50\u529b\u5b66\u7684\u57fa\u7840\u4e4b\u4e0a\u3002<\/span><\/section>\n

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\u5728\u5e7f\u4e49\u6b63\u5219\u70ed\u5316\u7814\u7a76\u4e2d\uff0c\u7cfb\u7edf\u548c\u73af\u5883\u4e4b\u95f4\u7684\u7ea0\u7f20\u4f1a\u626e\u6f14\u91cd\u8981\u7684\u89d2\u8272\u3002\u5982\u679c\u7cfb\u7edf\u548c\u73af\u5883\u5904\u4e8e\u7b80\u5355\u7684\u76f4\u79ef\u6001\u4e0a\uff0c\u7ea6\u5316\u540e\u7684\u7cfb\u7edf\u72b6\u6001\u4e0d\u4f1a\u662f\u6b63\u5219\u7cfb\u7efc\u7684Gibbs\u5206\u5e03\u3002\u56e0\u6b64\uff0c\u6ee1\u8db3\u5e7f\u4e49\u70ed\u5316\u7684\u72b6\u6001\u4e00\u5b9a\u662f\u7cfb\u7edf\u548c\u73af\u5883\u4e4b\u95f4\u7684\u7ea0\u7f20\u6001\u3002\u6587\u732e[72-74]\u7814\u7a76\u7684\u7cfb\u7edf\u548c\u73af\u5883\u4e4b\u95f4\u65e0\u76f8\u4e92\u4f5c\u7528\uff0c\u800c\u7b14\u8005\u56e2\u961f\u7684\u5de5\u4f5c\u8bc1\u660e\u76f8\u4e92\u4f5c\u7528\u7684\u51fa\u73b0\u4f7f\u5f97\u7b49\u80fd\u58f3\u5c42\u53d8\u5f62\u3002\u5728\u53d8\u5f62\u7684\u7b49\u80fd\u58f3\u5c42\u5185\uff0c\u5bf9\u73af\u5883\u53d6\u5e73\u5747\u5f97\u5230\u7684\u7cfb\u7edf\u7ea6\u5316\u5bc6\u5ea6\u77e9\u9635\u4e0d\u518d\u662f\u6b63\u5219\u7684\uff0c\u53d8\u5f62\u4f1a\u4f7f\u5f97\u5728\u5c0f\u7cfb\u7edf\u7684\u70ed\u5316\u6001\u4e0a\u4ea7\u751f\u4e00\u4e2a\u7070\u5ea6<\/span>\u56e0\u5b50[75]\uff0c<\/span>\u5f71\u54cd\u7ea6\u5316\u7cfb\u7edf\u7684\u6e29\u5ea6\u3002<\/span><\/section>\n

<\/section>\n
\u5e7f\u4e49\u6b63\u5219\u70ed\u5316\u7684\u4e00\u4e2a\u91cd\u8981\u5e94\u7528\u662f\u89e3\u91ca\u9ed1\u6d1e\u975e\u70ed\u8f90\u5c04\u8c31\u548c\u9ed1\u6d1e\u4fe1\u606f\u4e22\u5931\u4e4b\u8c1c<\/span><\/strong>\u30022000 \u5e74Parikh \u548c Wilcz<\/span>ek[76]\u5229<\/span>\u7528\u96a7\u7a7f\u7406\u8bba\u5f97\u5230\u5c0f\u8d28\u91cfSchwarzschild\u9ed1\u6d1e\u7684\u975e\u5e73\u8861\u8f90\u5c04\u8c31\u3002\u8d28\u91cf\u4e3aM<\/em>\u7684\u9ed1\u6d1e\u8f90\u5c04\u80fd\u91cf\u4e3a\u03c9<\/em>\u7684\u7c92\u5b50\u540e\uff0c\u8d28\u91cfM<\/em>\u6539\u53d8\u4e3aM<\/em>–\u03c9<\/em>\u4f1a\u5f71\u54cd\u8f90\u5c04\u540e\u7684\u65f6\u7a7a\u5ea6\u89c4\uff0c\u5e76\u76f4\u63a5\u5f71\u54cd\u518d\u8f90\u5c04\u7684\u6982\u7387\u5206\u5e03\uff0c\u5bfc\u81f4\u975e\u6b63\u5219\u70ed\u6001\uff1a<\/span><\/section>\n

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\u5219\u8f90\u5c04\u5206\u5e03\u4e0d\u4ec5\u4e0e\u9ed1\u6d1e\u8d28\u91cf\u6709\u5173\uff0c\u8fd8\u4e0e\u8f90\u5c04\u7c92\u5b50\u672c\u8eab\u7684\u80fd\u91cf\u6709\u5173\u3002\u540e\u6765\u8521<\/span>\u5e86\u5b87\u7b49[77,78]\u53d1<\/span>\u73b0\uff0c\u8fd9\u79cd\u975e\u70ed\u5206\u5e03\u5b9e\u9645\u4e0a\u5305\u542b\u4e86\u8f90\u5c04\u7c92\u5b50\u4e4b\u95f4\u7684\u5173\u8054\u4fe1\u606f\uff0c\u53ef\u4ee5\u7528\u6765\u89e3\u91ca\u9ed1\u6d1e\u4fe1\u606f\u4e22\u5931\u4e4b\u8c1c\u3002\u4ed6\u4eec\u8ba1\u7b97\u4e86\u80fd\u91cf\u5206\u522b\u4e3a\u03c9<\/em>1<\/sub>\u548c\u03c9<\/em>2<\/sub>\u7684\u4e24\u6b21\u8f90\u5c04\u4e4b\u95f4\u7684\u5173\u8054\u71b5S<\/em>(\u03c9<\/em>1<\/sub>\uff1a\u03c9<\/em>2<\/sub>)=8\u03c0\u03c9<\/em>1<\/sub>\u03c9<\/em>2<\/sub>\uff0c\u5176\u4e2d\u5355\u6b21\u8f90\u5c04\u71b5S<\/em>(\u03c9<\/em>)=\u2212ln\u0393<\/em>(\u03c9<\/em>)\u3002\u8fd9\u610f\u5473\u7740\u4ece\u9ed1\u6d1e\u89c6\u754c\u5148\u540e\u8f90\u5c04\u51fa\u7684\u7c92\u5b50\u4e4b\u95f4\u5b58\u5728\u5173\u8054\uff0c\u5173\u8054\u5927\u5c0f\u6b63\u6bd4\u4e8e\u4e24\u4e2a\u7c92\u5b50\u7684\u80fd\u91cf\u3002\u5728\u6b64\u57fa\u7840\u4e0a\u53ef\u4ee5\u5f97\u5230\u9ed1\u6d1e\u8f90\u5c04\u7684\u7ea7\u8054\u516c\u5f0f\uff1a<\/span><\/section>\n

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\u5176\u4e2dS(\u03c9<\/em>2<\/sub>|\u03c9<\/em>1<\/sub>)\u662f\u6761\u4ef6\u8f90\u5c04\u71b5\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u5f53\u9ed1\u6d1e\u5b8c\u5168\u8f90\u5c04\u6389 (\u2211\u03c9i <\/sub><\/em>= M<\/em>) \u65f6\uff0c\u8f90\u5c04\u7684\u5173\u8054\u71b5\u5c31\u662f\u539f\u521d\u7684\u9ed1\u6d1e\u71b5\uff0cS(\u03c9<\/em>1<\/sub>,\u03c9<\/em>2<\/sub>,\u22ef,\u03c9n<\/sub><\/em>)=4\u03c0M<\/em>2<\/sup>\u3002\u56e0\u6b64\uff0c\u57fa\u4e8e\u4e0a\u8ff0\u5173\u8054\u4fe1\u606f\u53ef\u4ee5\u89e3\u51b3\u9ed1\u6d1e\u8f90\u5c04\u4e2d\u7684\u4fe1\u606f\u4e22\u5931\u95ee\u9898\uff0c\u5373\u9ed1\u6d1e\u8f90\u5c04\u4e22\u5931\u7684\u4fe1\u606f\u5b8c\u5168\u8f6c\u5316\u4e3a\u8f90\u5c04\u7c92\u5b50\u95f4\u7684\u5173\u8054\u3002<\/span><\/section>\n

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\u4ed4\u7ec6\u5206\u6790\u8521\u5e86\u5b87\u7b49[77]\u7684\u5f00\u521b\u6027\u5de5\u4f5c\uff0c\u672c\u6587\u4e24\u4f4d\u4f5c\u8005\u610f\u8bc6\u5230\u5982\u6b64\u590d\u6742\u7684\u9ed1\u6d1e\u5ea6\u89c4\u7ed9\u51fa\u7684\u8f90\u5c04\u7c92\u5b50\u4e4b\u95f4\u5173\u8054\u65b9\u5f0f\u5c45\u7136\u90fd\u76f8\u540c\uff0c\u5e73\u8861\u60c5\u51b5\u8f90\u5c04\u7684\u975e\u6b63\u5219\u5f62\u5f0f\u4e00\u5b9a\u4e0e\u9ed1\u6d1e\u7684\u65f6\u7a7a\u51e0\u4f55\u65e0\u5173\u3002\u57fa\u4e8e\u975e\u6b63\u5219\u70ed\u5316\u7684\u5de5\u4f5c\uff0c\u4ed6\u4eec\u4e0e\u8521\u5e86\u5b87\u5408\u4f5c\uff0c\u4ece\u9ed1\u6d1e\u7684\u201c\u4e00\u6bdb\u201d\u5b9a\u7406\u51fa\u53d1\uff0c\u4e24\u6b21\u7ea7\u8054\u8f90\u5c04<\/span> (\u5148\u540e\u80fd\u91cf\u4e3a\u03c9<\/em>1<\/sub>\u548c\u03c9<\/em>2<\/sub>) <\/span>\u548c\u4e00\u6b21\u80fd\u91cf\u4e3a\u03c9<\/em>1<\/sub>+\u03c9<\/em>2<\/sub>\u5355\u8f90\u5c04\u7684\u7b49\u4ef7\u6027\uff0c\u4e00\u822c\u5730\u63a8\u5bfc\u51fa\u4e86\u9ed1\u6d1e\u8f90\u5c04\u7684\u975e\u6b63\u5219\u5206\u5e03\u0393<\/em>(\u03c9<\/em>)[78]\u3002\u7814\u7a76\u5206\u6790\u8fd8\u628a\u9ed1\u6d1e\u7684\u81ea\u7531\u5ea6B<\/em>\u548c\u65f6\u7a7a\u5176\u4ed6\u90e8\u5206O<\/em>\u8003\u8651\u6210\u4e3a\u70ed\u5316\u73af\u5883\u3002\u5047\u8bbe\u6574\u4e2a\u5b87\u5b99\u5904\u5728\u4e00\u4e2a\u7eaf\u6001\uff1a<\/span><\/section>\n

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\u9ed1\u6d1e\u7684\u72b6\u6001\u5373\u662f\u03c1<\/em>B<\/sub>=TrO<\/em><\/sub>[|\u03a8 <\/em>\u27e9\u27e8\u03a8 <\/em>|]\uff0c\u6839\u636e\u524d\u9762\u5e7f\u4e49\u70ed\u5316\u7684\u8ba8\u8bba\u53ef\u4ee5\u77e5\u9053\u9ed1\u6d1e\u7684\u72b6\u6001\u8fd1\u4f3c\u4e3a\u4e00\u4e2a\u70ed\u6001\u3002\u518d\u628a\u8f90\u5c04\u672c\u8eab\u5f53\u4f5c\u7814\u7a76\u70ed\u529b\u5b66\u7cfb\u7edf\uff0c\u6839\u636e\u5e7f\u4e49\u6b63\u5219\u70ed\u5316\u7684\u601d\u60f3\uff0c\u5c31\u80fd\u4e00\u822c\u5730\u5f97\u5230\u9ed1\u6d1e\u8f90\u5c04\u80fd\u8c31\u7684\u975e\u70ed<\/span>\u5206\u5e03[79]\u3002\u8fd9<\/span>\u4e00\u7814\u7a76\u8868\u660e\uff0c\u8f90\u5c04-\u9ed1\u6d1e\u5173\u8054\u5bfc\u81f4\u7684\u9ed1\u6d1e\u975e\u70ed\u8f90\u5c04\u8c31\u662f\u6709\u9650\u7cfb\u7edf\u7edf\u8ba1\u7684\u5fc5\u7136\u7ed3\u679c\u3002<\/span><\/section>\n

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\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u7cfb\u7edf\u52a0\u73af\u5883\u7684\u6574\u4e2a\u6001\u7a7a\u95f4\u4e2d\uff0c\u8fd8\u5b58\u5728\u4e00\u90e8\u5206\u4e0d\u6ee1\u8db3\u6b63\u5219\u5178\u578b\u6027\u7684\u72b6\u6001\u3002\u8fd1\u4e9b\u5e74\u6765\uff0c\u5173\u4e8e\u672c\u5f81\u6001\u70ed\u5316\u5047\u8bf4<\/span> (eigenstate thermalization hypothesis)<\/span> \u7684\u7814\u7a76[80,81] \u63a2\u8ba8\u4e86\u7cfb\u7edf\u5982\u4f55\u4ece\u8fd9\u90e8\u5206\u4e0d\u6ee1\u8db3\u6b63\u5219\u5178\u578b\u6027\u7684\u5c11\u6570\u72b6\u6001\u6f14\u5316\u5230\u6ee1\u8db3\u6b63\u5219\u5178\u578b\u6027\u7684\u72b6\u6001\uff0c\u4e3a\u6709\u9650\u7cfb\u7edf\u70ed\u5316\u95ee\u9898\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u5d2d\u65b0\u7684\u601d\u8def\u3002<\/span><\/section>\n<\/section>\n

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5. \u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u7406\u60f3Carnot\u5faa\u73af\u7ed9\u51fa\u4e86\u6240\u6709\u70ed\u529b\u5b66\u5faa\u73af\u6548\u7387\u7684\u57fa\u672c\u9650\u5236\uff0c\u675c\u7edd\u4e86\u4e00\u5927\u7c7b\u6c38\u52a8\u673a\u7684\u5c1d\u8bd5\uff0c\u662f\u70ed\u529b\u5b66\u53d1\u5c55\u7684\u91cc\u7a0b\u7891\u3002Carnot\u5faa\u73af\u662f\u5efa\u7acb\u5728\u4e00\u7ec4\u51c6\u9759\u6001\u8fc7\u7a0b\u57fa\u7840\u4e0a\u7684\u70ed\u529b\u5b66\u5faa\u73af\uff0c\u5176\u4e2d\u5728\u4e24\u4e2a\u5206\u522b\u4e0e\u9ad8\u3001\u4f4e\u6e29\u70ed\u6e90\u63a5\u89e6\u7684\u7b49\u6e29\u8fc7\u7a0b\u4e2d\uff0c\u8981\u65e0\u7a77\u7f13\u6162\u5730\u64cd\u63a7\u6c14\u4f53\u4f53\u79ef\uff0cCarnot\u5faa\u73af\u9700\u8981\u7684\u65f6\u95f4\u539f\u5219\u4e0a\u662f\u65e0\u7a77\u957f\uff0c\u8fd9\u4f7f\u5f97\u7406\u60f3Carnot\u5faa\u73af\u7684\u5728\u5355\u4f4d\u65f6\u95f4\u5185\u8f93\u51fa\u4e3a\u96f6\uff0c\u5373\u529f\u7387\u4e3a\u96f6\u3002\u7136\u800c\uff0c\u5728\u5b9e\u9645\u7684\u5e94\u7528\u4e2d\uff0c\u901a\u5e38\u6700\u5927\u7684\u9700\u6c42\u662f\u70ed\u529b\u5b66\u8fc7\u7a0b\u6709\u8f83\u5927\u7684\u8f93\u51fa\u529f\u7387\uff0c\u4f8b\u5982\u6211\u56fd\u6700\u65b0\u88c5\u673a\u7684\u77f3\u5c9b\u6838\u7535\u7ad9\u7684\u4e00\u4e2a\u5173\u952e\u6307\u6807\u662f\u88c5\u673a\u529f\u7387\u3002\u9488\u5bf9\u8fd9\u4e00\u7c7b\u95ee\u9898\uff0c\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u5e94\u8fd0\u800c\u751f\uff0c\u5176\u6838\u5fc3\u76ee\u6807\u662f\u5f25\u5408\u7406\u60f3\u7684\u4f20\u7edf\u70ed\u529b\u5b66\u7406\u8bba\u548c\u5b9e\u9645\u5e94\u7528\u4e4b\u95f4\u7684\u9e3f\u6c9f\uff0c\u5e76\u63a8\u52a8\u975e\u5e73\u8861\u70ed\u529b\u5b66\u7684\u53d1\u5c55\uff0c\u5bf9\u8fd1\u5e73\u8861\u8fc7\u7a0b\u7ed9\u51fa\u5b9a\u91cf\u7684\u7ed3\u679c\u3002<\/span><\/section>\n

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5.1 \u529f\u7387-\u6548\u7387\u7ea6\u675f\u5173\u7cfb<\/strong><\/span><\/section>\n

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\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7684\u53d1\u5c55\u8087\u59cb\u4e8e\u6838\u7535\u80fd\u6e90\u7684\u53d1\u5c55\u3002\u572820\u4e16\u7eaa50\u5e74\u4ee3\uff0cYvo<\/span>n[82]\u9488<\/span>\u5bf9\u6838\u7535\u5faa\u73af\u5f97\u5230\u4e86\u6700\u5927\u529f\u7387\u8f93\u51fa\u65f6\u7684\u6548\u7387\u30021975\u5e74\uff0c\u9488\u5bf9\u6709\u9650\u65f6\u95f4\u7684Carnot\u5faa\u73af\uff0cCurzon\u548cAhlbor<\/span>n[83]\u5229<\/span>\u7528\u6052\u5b9a\u70ed\u529b\u5b66\u6d41\u7684\u5047\u8bbe\uff0c\u5f97\u5230\u4e86\u540e\u6765\u5e7f\u4e3a\u4eba\u77e5\u7684CA\u6548\u7387\uff0c\u03b7<\/em>CA<\/sub>=1\u2212\u221a(T<\/em>c<\/sub>\/T<\/em>h<\/sub>)\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\u8be5\u6548\u7387\u4e0d\u4f9d\u8d56\u4e8e\u5faa\u73af\u4e2d\u7269\u8d28\u7684\u7279\u6027\uff0c\u5177\u6709\u76f8\u5f53\u7684\u666e\u9002\u6027\uff0c\u56e0\u800c\u5f97\u5230\u4e86\u5e7f\u6cdb\u7684\u5173\u6ce8\uff0c\u5e76\u572820\u4e16\u7eaa\u4e03\u516b\u5341\u5e74\u4ee3\u5f15\u53d1\u4e86\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7814\u7a76\u7684\u70ed<\/span>\u6f6e[84,85]<\/span>\u3002<\/span><\/section>\n

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\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u8fc7\u7a0b\u901a\u5e38\u4f34\u968f\u7740\u989d\u5916\u71b5<\/span> (\u5373\u4e0d\u53ef\u9006\u71b5) <\/span>\u4ea7\u751f\uff0c\u65f6\u95f4\u8d8a\u957f\u989d\u5916\u71b5\u4ea7\u751f\u8d8a\u5c11\u3002\u5728\u8fd1\u4e9b\u5e74\u53d1\u5c55\u7684\u4f4e\u8017\u6563<\/span>\u6a21\u578b[86]\u4e2d\uff0c\u5de5\u4f5c<\/span>\u7269\u8d28\u5728\u4e24\u4e2a\u6709\u9650\u65f6\u95f4\u7b49\u6e29\u8fc7\u7a0b\u4e2d\u5438\u6536\u7684\u70ed\u91cf\u8868\u8fbe\u6210\u5982\u4e0b\uff1a<\/span><\/section>\n

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\u5bf9\u4e8e\u4efb\u610f\u7ed9\u5b9a\u7684\u8f93\u51fa\u529f\u7387P<\/em>\uff0c\u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\u7684\u6548\u7387\u4e0d\u4ec5\u5b58\u5728\u4e0a\u9650\uff0c\u800c\u4e14\u8fd8\u5b58\u5728\u4e0b\u9650\u3002\u6211<\/span>\u4eec[87]\u63a8<\/span>\u5bfc\u51fa\u4e00\u822c\u5f97\u5230\u6548\u7387\u548c\u529f\u7387\u7ea6\u675f\u5173\u7cfb\uff1a<\/span><\/section>\n

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\u5176\u4e2d\u03b7\u0303<\/em>=\u03b7<\/em>\/\u03b7<\/em>C<\/sub>\u548cP\u0303<\/em>=P<\/em>\/P<\/em>max<\/sub>\u5206\u522b\u662f\u4ee5\u03b7<\/em>C<\/sub>\u548cP<\/em>max<\/sub>\u4e3a\u5355\u4f4d\u7684\u7ea6\u5316\u6548\u7387\u548c\u529f\u7387\u3002\u8fd9\u4e2a\u529f\u7387\u6548\u7387\u7ea6\u675f\u5173\u7cfb\u662f\u4e00\u4e2a\u4e0d\u4f9d\u8d56\u4e8e\u5de5\u4f5c\u7269\u8d28\u7684\u666e\u9002\u5173\u7cfb\uff0c\u5bf9\u4efb\u610f\u60c5\u51b5\u6210\u7acb\u3002\u6b64\u524d Ryabov\u548cHolub<\/span>ec[88,89]\u7ed9<\/span>\u51fa\u7684\u8fd1\u4f3c\u7684\u7ea6\u675f\u5173\u7cfb\u4ec5\u4ec5\u5bf9P\u0303<\/em>\u22480\u548cP\u0303<\/em>\u22481\u8303\u56f4\u6210\u7acb\u3002\u56fe10\u5c55\u793a\u4e86\u4e0a\u8ff0\u7ea6\u675f\u5173\u7cfb\uff0c\u5176\u4e2d\u84dd\u70b9\u4ee3\u8868\u4ee5\u4e8c\u80fd\u7ea7\u539f\u5b50\u4e3a\u5de5\u4f5c\u7269\u8d28\u7684\u70ed\u529b\u5b66\u5faa\u73af\u7684\u529f\u7387\u548c\u6548\u7387\uff0c\u7ea2\u7ebf\u548c\u7070\u7ebf\u5206\u522b\u4ee3\u8868\u4e86\u7ea6\u675f\u5173\u7cfb\u7684\u4e0a\u9650\u548c\u4e0b\u9650\u3002\u56fe10\u8bf4\u660e\u5229\u7528\u4f4e\u8017\u65631\/\u03c4<\/em>\u5047\u8bbe\u5f97\u5230\u7684\u7ea6\u675f\u5173\u7cfb\u5bf9\u4e8e\u91cf\u5b50\u70ed\u529b\u5b66\u5faa\u73af\u540c\u6837\u9002\u7528\u3002<\/span><\/section>\n

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\u56fe10 \u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\u7684\u529f\u7387\u6548\u7387\u7ea6\u675f\u5173\u7cfb  (a)\u57fa\u4e8e\u4e8c\u80fd\u7ea7\u7cfb\u7edf\u7684\u6709\u9650\u65f6\u95f4\u91cf\u5b50Carnot\u5faa\u73af\uff1b(b)\u91cf\u5b50Carnot\u5faa\u73af\u4e2d\u529f\u7387-\u6548\u7387\u548c\u4e00\u822c\u7ea6\u675f\u5173\u7cfb\u7684\u5bf9\u6bd4\uff0c\u5176\u4e2d\u56fe\u4e2d\u7684\u68d5\u8272\u865a\u7ebf\u548c\u7070\u8272\u70b9\u7ebf\u662f\u7531(25)\u5f0f\u7ed9\u51fa\uff0c\u7eff\u8272\u4e09\u89d2\u4ee3\u8868\u6700\u5927\u529f\u7387\u7684\u4f4d\u7f6e<\/span><\/section>\n<\/section>\n
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\u5728\u4f20\u7edf\u7684\u51c6\u9759\u6001\u70ed\u529b\u5b66\u5faa\u73af\u4e2dCarnot\u5faa\u73af\u7684\u6548\u7387\u6700\u9ad8\uff0c\u4f46\u5728\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u8fc7\u7a0b\u4e2d\u8be5\u7ed3\u8bba\u4e0d\u518d\u6210\u7acb\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u5728\u4e8c\u8005\u90fd\u5728\u6700\u5927\u529f\u7387\u6761\u4ef6\u4e0b\uff0cOtto\u5faa\u73af\u7684\u6548\u7387\u5728\u4e00\u4e9b\u53c2\u6570\u533a\u95f4\u5185\u4f1a\u660e\u663e\u4f18\u4e8eCarnot\u5faa\u73af\u3002\u7279\u522b\u5728\u6e29\u5dee\u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\uff0c\u901a\u8fc7Otto\u70ed\u529b\u5b66\u5faa\u73af\u66f4\u5bb9\u6613\u83b7\u5f97\u66f4\u9ad8\u7684<\/span>\u6548\u7387[90,91]<\/span>\u3002<\/span><\/section>\n

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\u4f4e\u8017\u6563\u6a21\u578b\u4e4b\u6240\u4ee5\u80fd\u5728\u8fd1\u4e9b\u5e74\u6380\u8d77\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7814\u7a76\u7684\u65b0\u6f6e\u6d41<\/span>\uff0c\u662f\u56e0\u4e3a\u6b64\u6a21\u578b\u80fd\u591f\u628a\u5916\u754c\u7684\u63a7\u5236\u65b9\u5f0f\u548c\u52a8\u529b\u5b66\u6f14\u5316\u7eb3\u5165\u70ed\u529b\u5b66\u7814\u7a76\u7684\u6846\u67b6\u4e2d[92]\u3002\u5728\u6709\u9650<\/span>\u65f6\u95f4\u7b49\u6e29\u8fc7\u7a0b\u4e2d\uff0c\u4e0e\u4e0d\u53ef\u9006\u71b5\u4ea7\u751f\u5173\u8054\u7684\u53c2\u6570\u03a3<\/em>h<\/sub>\u548c\u03a3<\/em>c<\/sub>\u4e0e\u63a7\u5236\u7684\u8fc7\u7a0b\u76f4\u63a5\u76f8\u5173\u3002\u5bf9\u4e8e\u4e8c\u80fd\u7ea7\u91cf\u5b50\u7cfb\u7edf\uff0c\u53c2\u6570\u03a3<\/em>h<\/sub>=\u0398\u03be<\/em>\uff0c\u5176\u4e2d\u0398<\/em>=\u03b2<\/em>h<\/sub>2<\/sup>(\u03c9<\/em>h<\/sub>f<\/sup>\u2212\u03c9<\/em>h<\/sub>i<\/sup>)2<\/sup>\/8\u4e0e\u7cfb\u7edf\u521d\u672b\u72b6\u6001\u53c2\u6570\u4ee5\u53ca\u73af\u5883\u6e29\u5ea6\u6709\u5173\uff0c\u03be<\/em>=\u27e8v<\/em>2<\/sup>\u27e9\/\u27e8v<\/em>\u27e92<\/sup>\u4e0e\u53c2\u6570\u63a7\u5236\u901f\u5ea6v<\/em>\u7684\u6da8\u843d\u76f8\u5173\u3002\u6b64\u540e\uff0c\u6709\u66f4\u591a\u7684\u7814\u7a76\u5c06\u70ed\u529b\u5b66\u8fc7\u7a0b\u63a7\u5236\u7eb3\u5165\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7684\u7814\u7a76\u4e2d\uff0c\u5176\u4e2d\u8574\u542b\u4e86\u540e\u6587\u63d0\u53ca\u7684\u70ed\u529b\u5b66\u957f\u5ea6\u7b49\u6982\u5ff5\u3002<\/span><\/section>\n

<\/section>\n
5.2 \u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u5b9e\u9a8c<\/strong><\/span><\/section>\n

<\/section>\n
\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7684\u7814\u7a76\u53d6\u5f97\u4e86\u5927\u91cf\u7684\u7814\u7a76\u6210\u679c\uff0c\u5b83\u4eec\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u4f7f\u7528\u4e86\u524d\u8ff0\u7684\u4f4e\u8017\u6563\u6a21\u578b\u5047\u8bbe\uff0c\u5373\u4e0d\u53ef\u9006\u71b5\u76841\/\u03c4<\/em>\u6807\u5ea6\u5173\u7cfb\u3002\u5728\u7269\u7406\u4e0a\uff0c\u4f4e\u8017\u6563\u6a21\u578b\u548c\u70ed\u529b\u5b66\u7cfb\u7edf\u7ebf\u6027\u76f8\u5e94\u7406\u8bba\u662f\u7b49\u4ef7\u7684\uff0c\u56e0\u6b641\/\u03c4<\/em>\u6807\u5ea6\u5173\u7cfb\u662f\u957f\u65f6\u8fd1\u4f3c\u7684<\/span>\u7ed3\u679c[93]\u3002<\/span>\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7684\u7406\u8bba\u548c\u5b9e\u9a8c\u5fc5\u987b\u5173\u6ce8\u8be5\u6807\u5ea6\u5173\u7cfb\u5728\u591a\u5927\u8303\u56f4\u5185\u9002\u7528\u3002\u5176\u5b9e\u8fd1\u671f\u7406\u8bba\u4e0a\u6709\u5f88\u591a\u7684\u7814\u7a76\u4ece\u8fd0\u52a8\u65b9\u7a0b\u51fa\u53d1\uff0c\u7ed9\u51fa\u4e86\u6807\u5ea6\u5173\u7cfb\u7684\u6210\u7acb\u533a\u95f4\uff0c\u4f46\u662f\u5728\u5b9e\u9a8c\u4e0a\u5374\u9c9c\u6709\u8fd9\u65b9\u9762\u7684\u7814\u7a76\u6210\u679c\uff0c\u7a76\u5176\u539f\u56e0\u662f\u5b9e\u9a8c\u5e73\u53f0\u7684\u7f3a\u4e4f\u3002\u6700\u8fd1\uff0c\u5728\u4e00\u4e9b\u5fae\u89c2\u5b9e\u9a8c\u7684<\/span>\u5e73\u53f0\u4e0a[20]\uff0c<\/span>\u5df2\u6709\u5c11\u6570\u5b9e\u9a8c\u5f00\u59cb\u5173\u6ce8\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u3002<\/span><\/section>\n

<\/section>\n
3\u5e74\u524d\uff0c\u6211<\/span>\u4eec[94]\u57fa<\/span>\u4e8e\u7406\u60f3\u6c14\u4f53\u642d\u5efa\u4e86\u4e00\u4e2a\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u5b9e\u9a8c\u5e73\u53f0\u3002\u5b9e\u9a8c\u88c5\u7f6e\u4e2d\u7684\u5de5\u4f5c\u7269\u8d28\u662f\u5e72\u71e5\u7a7a\u6c14\uff0c\u5176\u72b6\u6001\u7531\u7406\u60f3\u6c14\u4f53\u72b6\u6001\u65b9\u7a0b\u63cf\u8ff0\u3002\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u8fc7\u7a0b\u901a\u8fc7\u6b65\u8fdb\u7535\u673a\u8fdb\u884c\u7cbe\u786e\u63a7\u5236\u3002\u5bf9\u4e8e\u7406\u60f3\u6c14\u4f53\u800c\u8a00\uff0c\u4e00\u65e6\u83b7\u5f97\u6c14\u4f53\u7684\u538b\u5f3aP<\/em>\u548c\u4f53\u79efV<\/em>,\u5c31\u53ef\u4ee5\u8ba1\u7b97\u51fa\u6c14\u4f53\u7684\u6e29\u5ea6T<\/em>\uff0c\u8fdb\u800c\u83b7\u5f97\u6c14\u4f53\u7684\u5185\u80fd\u53d8\u5316\u3002<\/span><\/section>\n

<\/section>\n
\u901a\u5e38\u53ef\u4ee5\u7528\u4e0d\u53ef\u9006\u505a\u529f\u6765\u5ea6\u91cf\u6709\u9650\u65f6\u95f4\u8fc7\u7a0b\u7684\u4e0d\u53ef\u9006\u6027\uff0cW<\/em>irr<\/sub>(\u03c4<\/em>)=W<\/em>(\u03c4<\/em>)\u2212\u0394F<\/em>\uff0c\u5176\u4e2d\u0394F<\/em>\u662f\u7cfb\u7edf\u7684\u81ea\u7531\u80fd\u7684\u53d8\u5316\u3002\u5f53\u64cd\u63a7\u901f\u5ea6V<\/em>\u02d9<\/sup>\/V<\/em>\u8fdc\u5927\u4e8e\u6c14\u4f53\u7684\u5f1b\u8c6b\u901f\u7387\uff0c\u5373 (\u03b3<\/em>\u22121)t<\/em>r<\/sub>V<\/em>\u02d9<\/sup>\/V<\/em>\u226a1\uff0c\u4e0d\u53ef\u9006\u505a\u529f\u4e5f\u5177\u67091\/\u03c4<\/em>\u5173\u7cfb\u3002\u5176\u4e2d\u03b3<\/em>\u662f\u6c14\u4f53\u7684\u7edd\u70ed\u7cfb\u6570\uff0ct<\/em>r<\/sub>\u662f\u6c14\u4f53\u7684\u70ed\u5f1b\u8c6b\u7684\u7279\u5f81\u65f6\u95f4\u3002\u56fe11\u5c55\u793a\u4e86\u5728\u6e29\u5ea6\u4e3a50 \u2103\u4e0b\u538b\u7f29\u7406\u60f3\u6c14\u4f53\u505a\u529f\u968f\u8fc7\u7a0b\u65f6\u95f4\u03c4<\/em>\u7684\u53d8\u5316\u5173\u7cfb\uff0c\u5b9e\u9a8c\u6570\u636e\u8bc1\u5b9e\uff0c\u957f\u65f6\u95f4\u53ef\u9006\u505a\u529f\u968f\u65f6\u95f4\u6309\u71671\/\u03c4<\/em>\u6807\u5ea6\u5173\u7cfb\u8870\u51cf\uff1b\u4e0d\u53ef\u9006\u71b5\u505a\u529f\u53ef\u4ee5\u901a\u8fc7\u538b\u7f29\u7a7a\u6c14\u7684\u65b9\u5f0f\u6765\u6539\u53d8\uff0c\u5728\u65f6\u95f4\u4e00\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u5300\u901f\u5730\u538b\u7f29\u8fc7\u7a0b\u4e2d\u4e0d\u53ef\u9006\u505a\u529f\u660e\u663e\u4f4e\u4e8e\u4ee5\u591a\u9879\u5f0f\u65b9\u5f0f\u538b\u7f29\u6c14\u4f53\u7684\u505a\u529f\u3002\u8fd9\u4e2a\u7ed3\u679c\u8868\u660e\uff0c\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u8fc7\u7a0b\u7684\u64cd\u7eb5\u65b9\u5f0f\u5bf9\u4e8e\u8c03\u8282\u70ed\u529b\u5b66\u8fc7\u7a0b\u5341\u5206\u91cd\u8981\u3002\u56e0\u6b64\uff0c\u8fd9\u4e2a\u7814\u7a76\u5de5\u4f5c\u4e3a\u4f18\u5316\u70ed\u80fd\u6e90\u8f6c\u5316\u8fc7\u7a0b\u63d0\u4f9b\u4e86\u65b0\u601d\u8def\u3002<\/span><\/section>\n

<\/span><\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n
\n
\u56fe11 \u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b661\/\u03c4<\/em>\u5173\u7cfb\u7684\u5b9e\u9a8c\u9a8c\u8bc1   (a) \u6e29\u5ea650 \u2103\u4e0b\u505a\u529f\u76841\/\u03c4<\/em>\u6807\u5ea6\u5173\u7cfb\uff1b(b) \u6807\u5ea6\u5173\u7cfb\u7684\u7cfb\u6570\u5bf9\u64cd\u63a7\u65b9\u5f0f\u7684\u4f9d\u8d56\u5173\u7cfbL<\/em>(t<\/em>)=L<\/em>0<\/sub>\u221dt<\/em>\u03b1<\/sup><\/em>\uff0c\u80fd\u91cf\u635f\u8017\u6700\u4f18\u64cd\u63a7\u662f\u5300\u901f\u63a7\u5236\u03b1<\/em>=1<\/span><\/section>\n<\/section>\n
\n

<\/span><\/section>\n
\u8fd1\u4e9b\u5e74\u70ed\u529b\u5b66\u5b9e\u9a8c\u7684\u4e00\u4e2a\u91cd\u8981\u65b9\u5411[95-97]\u662f\u9a8c\u8bc1\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u5faa\u73af\u8fc7\u7a0b\u7684\u529f\u7387\u548c\u6548\u7387\u7ea6\u675f\u5173\u7cfb\u3002\u57fa\u4e8e\u642d\u5efa\u7684\u7406\u60f3\u6c14\u4f53\u7684\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u5e73\u53f0\uff0c\u6211<\/span>\u4eec[98]\u8bbe\u8ba1<\/span>\u5b8c\u6574\u7684\u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\uff0c\u5e76\u5b9a\u91cf\u5730\u9a8c\u8bc1\u4e86\u529f\u7387-\u6548\u7387\u7ea6\u675f\u5173\u7cfb\u3002\u5faa\u73af\u4e2d\u4e24\u4e2a\u7b49\u6e29\u8fc7\u7a0b\u5206\u522b\u5728\u4e0d\u540c\u7684\u6e29\u5ea6\u7684\u70ed\u6d74\u4e2d\u5b8c\u6210\uff0c\u5728\u6d4b\u5f97\u76f8\u5e94\u7684\u505a\u529f\u548c\u5438\u653e\u70ed\u7684\u540c\u65f6\uff0c\u4fdd\u8bc1\u4e86\u7b49\u6e29\u8fc7\u7a0b\u7684\u672b\u6001\u548c\u53e6\u4e00\u4e2a\u7b49\u6e29\u8fc7\u7a0b\u7684\u521d\u6001\u901a\u8fc7\u4e00\u4e2a\u7edd\u70ed\u8fc7\u7a0b\u8fde\u63a5\u8d77\u6765\uff0c\u5b9e\u73b0\u4e86\u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\u3002\u56fe12\u5c55\u793a\u4e86\u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\u7684\u8fc7\u7a0b\u548c\u70ed\u529b\u5b66\u5faa\u73af\u7684\u529f\u7387-\u6548\u7387\u7ea6\u675f\u5173\u7cfb\u3002\u8bc4\u4f30\u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\u7684\u5173\u952e\u91cf\u662f\u6700\u5927\u529f\u7387\u6548\u7387\u3002\u6211\u4eec\u63d0\u53d6\u4e86\u5b9e\u9a8c\u4e2d\u6240\u6709\u6e29\u5ea6\u7ec4\u5408\u7684\u6700\u5927\u529f\u7387\u6548\u7387\uff0c\u5e76\u5728\u56fe12(c)\u4e2d\u5c55\u793a\u5176\u4e0eCarnot\u6548\u7387\u7684\u5173\u7cfb\u3002\u83b7\u5f97\u7684\u6700\u5927\u6548\u7387<\/span> (\u5e26\u6709\u8bef\u5dee\u68d2\u7684\u6807\u8bb0) <\/span>\u9075\u5faa\u4e00\u4e2a\u7b80\u5355\u7684\u5173\u7cfb\u03b7<\/em>EMP<\/sub> = (0.524 \u00b1 0.034)\u03b7<\/em>C<\/sub>\u3002\u5b83\u4e0e\u5404\u79cd\u6709\u9650\u65f6\u95f4\u5faa\u73af\u6a21\u578b\u7684\u6700\u5927\u529f\u7387\u6548\u7387\u5728Carnot\u6548\u7387\u03b7<\/em>C<\/sub>\u7684\u4e00\u9636\u9879\u4e0a\u5f88\u597d\u5730\u7b26\u5408\u3002\u4f8b\u5982\uff0c\u5728CA\u6a21\u578b\u4e2d\u03b7<\/em>CA<\/sub>\u548c\u4f4e\u8017\u6563\u6a21\u578b[86]\u7684\u03b7<\/em>C<\/sub>\/(2\u2212\u03b7<\/em>C<\/sub>)\u4e2d\uff0c\u7cfb\u65701\/2\u662f\u4e00\u4e2a\u72ec\u7acb\u4e8e\u7279\u5b9a\u7279\u5f81\u7684\u7ebf\u6027\u54cd\u5e94\u533a\u57df\u7684\u666e\u904d\u503c[99]\u3002\u6211\u4eec\u7684\u5b9e\u9a8c\u6570\u636e\u7cbe\u786e\u5730\u786e\u8ba4\u4e861\/2\u7cfb\u6570\u7684\u5b58\u5728\u3002<\/span><\/section>\n<\/section>\n

<\/section>\n
\n
<\/section>\n<\/section>\n
\n
\u56fe12 \u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af   (a)\u6709\u9650\u65f6\u95f4Carnot\u5faa\u73af\u7684\u5de5\u4f5c\u793a\u610f\u56fe\uff1b(b)\u5faa\u73af\u4e2d\u529f\u7387-\u6548\u7387\u7ea6\u675f\u5173\u7cfb\uff1b(c)\u6700\u5927\u529f\u7387\u6548\u7387\u5bf9Carnot\u6548\u7387\u7684\u4f9d\u8d56\u5173\u7cfb\u03b7<\/em>EMP<\/sub> = (0.524 \u00b1 0.034)\u03b7<\/em>C<\/sub><\/span><\/section>\n<\/section>\n
\n

<\/strong><\/span><\/section>\n
5.3 \u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7684\u51e0\u4f55\u63cf\u8ff0<\/strong><\/span><\/section>\n

<\/section>\n
\u5982\u524d\u6587\u6240\u8ff0\uff0c\u5728\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u8fc7\u7a0b\u4e2d\uff0c\u4ea7\u751f\u7684\u4e0d\u53ef\u9006\u6027\u662f\u8bc4\u4f30\u70ed\u529b\u5b66\u8fc7\u7a0b\u975e\u5e73\u8861\u7684\u4e00\u4e2a\u91cd\u8981\u6307\u6807\u3002\u901a\u5e38\u53ef\u4ee5\u4f7f\u7528\u4e0d\u53ef\u9006\u71b5\u4ea7\u751f\u6765\u8861\u91cf\uff0c\u4f8b\u5982\u5728\u4e00\u4e2a\u70ed\u5316\u7684\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u53ef\u9006\u7684\u71b5\u4ea7\u751f\u968f\u65f6\u95f4\u5355\u8c03\u9012\u589e\u3002\u4f4e\u8017\u6563\u6a21\u578b\u5047\u8bbe\u5728\u70ed\u4ea4\u6362\u8fc7\u7a0b\u4e2d\u4e0d\u53ef\u9006\u71b5\u7684\u53d8\u5316\u6ee1\u8db31\/\u03c4<\/em>\u6807\u5ea6\u5173\u7cfb\u3002\u5bf9\u4e8e\u76f4\u63a5\u53ef\u6d4b\u91cf\u7269\u7406\u91cf\uff0c\u4e0d\u53ef\u9006\u505a\u529f\u4e5f\u5b58\u57281\/\u03c4<\/em>\u6807\u5ea6\u5173\u7cfb\u3002\u4f20\u7edf\u70ed\u529b\u5b66\u548c\u7edf\u8ba1\u7269\u7406\u7684\u7814\u7a76\u8868\u660e\uff0c\u975e\u51c6\u9759\u6001\u8fc7\u7a0b\u5bf9\u4f53\u7cfb\u505a\u529f\u4f1a\u8d85\u8fc7\u4f53\u7cfb\u7684\u81ea\u7531\u80fd\u53d8\u5316\uff0c\u5373W<\/em>\u2a7e\u0394F<\/em>\u3002\u8fd1\u5e74\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u7814\u7a76\u628a\u6b64\u4e0d\u7b49\u5f0f\u66ff\u6362\u6210\u4e00\u4e2a\u5b9a\u91cf\u7684\u5173\u7cfbW <\/em>=\u0394F<\/em>+C<\/em>\/\u03c4<\/em>\uff0c\u5176\u4e2dC<\/em>\u2a7e0\u662f\u4e0e\u7cfb\u7edf\u521d\u672b\u6001\u4ee5\u53ca\u64cd\u63a7\u65b9\u5f0f\u6709\u5173\u7684\u53c2<\/span>\u6570[32]<\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u4e8b\u5b9e\u4e0a\uff0c\u4e0a\u8ff0\u5b9a\u91cf\u7684\u5173\u7cfb\u5728\u6709\u9650\u65f6\u95f4\u70ed\u529b\u5b66\u8fc7\u7a0b\u7814\u7a76\u4e2d\u81f3\u5173\u91cd\u8981\uff0c\u5b83\u7275\u6d89\u5230\u4e00\u4e2a\u63a7\u5236\u8fc7\u7a0b\u4e2d\u65f6\u95f4\u548c\u80fd\u91cf\u635f\u8017\u7684\u5236\u7ea6\u5173\u7cfb\uff0c\u5fc5\u7136\u6d89\u53ca\u4e8c\u8005\u4e4b\u95f4\u7684\u4f18\u5316\u5339\u914d\u95ee\u9898\u3002\u7ed9\u5b9a\u63a7\u5236\u65f6\u95f4\u03c4<\/em>\uff0c\u6211\u4eec\u5173\u5fc3\u7684\u662f\u5728\u591a\u5927\u7a0b\u5ea6\u4e0a\u80fd\u591f\u51cf\u5c0f\u80fd\u91cf\u635f\u8017\uff0c\u4ee5\u53ca\u76f8\u5173\u7684\u7406\u8bba\u6781\u9650\u95ee\u9898\u3002\u8fd9\u4e2a\u95ee\u9898\u7814\u7a76\u53ef\u4ee5\u8ffd\u6eaf\u5230\u65e9\u671f\u5173\u4e8e\u5e73\u8861\u6001\u70ed\u529b\u5b66\u8ddd\u79bb\u95ee\u9898\uff0c\u5373\u975e\u5e73\u8861\u8fc7\u7a0b\u7684\u80fd\u91cf\u635f\u8017\u6781\u5c0f\u503c\u600e\u4e48\u53d7\u9650\u4e8e\u5e73\u8861\u6001\u7a7a\u95f4\u7684\u51e0\u4f55\u5c5e\u6027\u3002\u5bf9\u4e8e\u7f13\u6162\u8c03\u63a7<\/span> (\u4f46\u975e\u51c6\u9759\u6001) <\/span>\u7684\u7b49\u6e29\u8fc7\u7a0b\uff0c\u7cfb\u7edf\u5728\u6f14\u5316\u8fc7\u7a0b\u4e2d\u7684\u6bcf\u4e00\u4e2a\u77ac\u95f4\u90fd\u63a5\u8fd1\u4e8e\u70ed\u5e73\u8861\u6001\uff0c\u5b83\u53ef\u4ee5\u8fd1\u4f3c\u5730\u7531\u4e00\u7ec4\u7cfb\u7edf\u7684\u5e73\u8861\u6001\u53c2\u6570\u63cf\u8ff0\uff0c\u6bd4\u5982\u7cfb\u7edf\u7684\u538b\u5f3a\u548c\u6e29\u5ea6\u3002\u5728\u8fd9\u6837\u8fd1\u5e73\u8861\u533a\u57df\u7684\u8fd1\u4f3c\u4e0b\uff0c\u4e0d\u53ef\u9006\u7a0b\u5ea6\u5c06\u666e\u9002\u5730\u53cd\u6bd4\u4e8e\u8c03\u63a7\u65f6\u95f4\uff0c\u53ef\u4ee5\u901a\u8fc7\u51e0\u4f55\u7684\u8bed\u8a00\u63cf\u8ff0\uff0c\u8fd9\u5c31\u5bfc\u81f4\u4e86\u70ed\u529b\u5b66\u957f\u5ea6\u7684\u6982\u5ff5[100]\u3002\u5728\u51e0\u4f55\u4e0a[101,102]\uff0c\u70ed\u529b\u5b66\u201c\u8ddd\u79bb\u201d\u6709\u660e\u786e\u7684\u7269\u7406\u610f\u4e49\uff1a\u5728\u8fd1\u5e73\u8861\u7684\u7f13\u6162\u9a71\u52a8\u4e0b\uff0c\u521d\u672b\u6001\u95f4\u7684\u70ed\u529b\u5b66\u957f\u5ea6\u7ed9\u51fa\u4e86\u5728\u6709\u9650\u65f6\u95f4\u5185\u5b8c\u6210\u7b49\u6e29\u8fc7\u7a0b\u6240\u6d88\u8017\u7684\u4e0d\u53ef\u9006\u529f\u4e0b\u9650[103-106]\u3002<\/span><\/section>\n

<\/section>\n
\u4e3a\u7b80\u5355\u8d77\u89c1\uff0c\u4ee5\u7406\u60f3\u6c14\u4f53\u4e3a\u4f8b\uff0c\u8bf4\u660e\u5e73\u8861\u6001\u7a7a\u95f4\u8ddd\u79bb\u548c\u975e\u5e73\u8861\u8fc7\u7a0b\u4e0d\u53ef\u9006\u6027\u4e4b\u95f4\u6709\u7279\u5b9a\u7684\u7ea6\u675f\u5173\u7cfb\u3002\u675f\u7f1a\u5728\u4e00\u4e2a\u4f53\u79ef\u4e3aV<\/em>\u7684\u7406\u60f3\u6c14\u4f53\u7684\u76f8\u7a7a\u95f4\u5206\u5e03\u6ee1\u8db3Maxwell\u5206\u5e03\u3002\u5bf9\u4e8e\u4f53\u79ef\u4e0d\u540c<\/span> (V<\/em>i<\/sub>\u548cV<\/em>f<\/sub>)<\/span> \u7684\u4e24\u4e2a\u5206\u5e03\uff0c\u901a\u8fc7Fisher\u4fe1\u606f\u5ea6\u89c4gVV<\/sub><\/em>\u5b9a\u4e49\u4e24\u4e2a\u5206\u5e03\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a<\/span><\/section>\n

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\u518d\u8003\u8651\u6e29\u5ea6\u4e3aT<\/em>e<\/sub>\u7684\u73af\u5883\u4e2d\u7406\u60f3\u6c14\u4f53\uff0c\u4eceV<\/em>i<\/sub>\u53d8\u5230V<\/em>f<\/sub>\uff0c\u5728\u6162\u901f\u63a7\u5236\u4e0b\u7684\u4e0d\u53ef\u9006\u529f\u4e3a<\/span><\/section>\n

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\n

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\u5176\u4e2dC<\/em>V<\/sub>\u662f\u7b49\u5bb9\u6bd4\u70ed\uff0c\u03b3<\/em>\u662f\u70ed\u4f20\u5bfc\u7cfb\u6570\u3002\u5229\u7528\u53d8\u5206\u539f\u7406\u53ef\u4ee5\u5f97\u5230\u5728V<\/em>\u02d9<\/sup>\/V<\/em>=Const\u65f6\uff0c\u4e0d\u53ef\u9006\u505a\u529f\u8fbe\u5230\u6700\u5c0f\u503c\uff0c\u5373W<\/em>irr,min<\/sub>\u221dD<\/em>2<\/sup>\u3002\u4ece\u8fd9\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u770b\u51fa\uff0c\u6700\u5c0f\u4e0d\u53ef\u9006\u505a\u529f\u548c\u5e73\u8861\u6001\u5206\u5e03\u7684\u8ddd\u79bb\u6709\u5173\uff0c\u4ee5\u4e0b\u5c06\u5bf9\u4e00\u7c7b\u70ed\u529b\u5b66\u8fc7<\/span>\u7a0b[107]\u7cbe\u786e<\/span>\u7ed9\u51fa\u8fd9\u79cd\u8054\u7cfb\u3002<\/span><\/section>\n

<\/section>\n
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<\/section>\n
\u8003\u8651\u4e00\u4e2a\u7269\u7406\u7cfb\u7edf\uff0c\u5176\u54c8\u5bc6\u987f\u91cf\u4e3a H<\/em>o<\/sub>(x<\/em>,p<\/em>,\u03bb<\/em>)=\u2211i<\/sub>p<\/em>i<\/sub>2<\/sup>\/2+U<\/em>o<\/sub>(x<\/em>,p<\/em>,\u03bb<\/em>)\u3002\u6211\u4eec\u5e0c\u671b\u65bd\u52a0\u8f85\u52a9\u63a7\u5236H<\/em>a<\/sub>(x<\/em>,p<\/em>,t<\/em>)=\u03bb<\/em>\u02d9<\/sup>\u22c5f<\/em>(x<\/em>,p<\/em>,\u03bb<\/em>)\uff0c\u4f7f\u5f97\u5728\u7ed9\u5b9a\u7684\u65f6\u95f4\u03c4<\/em>\uff0c\u628a\u53c2\u6570\u03bb<\/em>\u4ece\u03bb<\/em>i<\/sub>\u8c03\u63a7\u5230\u03bb<\/em>f<\/sub>\u4e0b\uff0c\u5e76\u4fdd\u6301\u7cfb\u7edf\u59cb\u7ec8\u5904\u5728\u70ed\u5e73\u8861\u6001\u4e0a\u3002\u6b64\u65f6\u7cfb\u7edf\u62d3\u5c55\u4e3a\u7531\u65b0\u54c8\u5bc6\u987f\u91cfH<\/em>0<\/sub>+H<\/em>a<\/sub>\u63cf\u8ff0\u7684\u65b0\u7cfb\u7edf\u3002\u5728\u8d77\u59cb\u548c\u672b\u4e86\u65f6\u523b\uff0c\u5c06\u8f85\u52a9\u52bf\u573aH<\/em>a<\/sub>(t<\/em>)\u64a4\u9664\uff0cH<\/em>a<\/sub>(0)=H<\/em>a<\/sub>(\u03c4<\/em>)=0\u3002\u8fd9\u6837\u4f7f\u5f97\u6269\u5c55\u7cfb\u7edf\u7684\u54c8\u5bc6\u987f\u91cf H<\/em>0<\/sub>+H<\/em>a<\/sub>\u7ed3\u675f\u65f6\u6070\u597d\u56de\u5230\u539f\u6765\u7684\u54c8\u5bc6\u987f\u91cfH<\/em>0<\/sub>\u3002\u540c\u65f6\u5728\u521d\u59cb\u548c\u672b\u4e86\u65f6\u523b\uff0c\u7cfb\u7edf\u5206\u5e03\u51fd\u6570\u6070\u597d\u5c31\u662f\u76f8\u5e94\u54c8\u5bc6\u987f\u91cf\u5bf9\u5e94\u7684\u5e73\u8861\u6001\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u53ef\u9006\u505a\u529f\u5199\u6210\u4e25\u683c\u7684\u4e8c\u6b21\u578b\u5f62\u5f0f\uff1a<\/span><\/section>\n

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\u6b64\u65f6\u5b9a\u4e49\u63cf\u8ff0\u4e0d\u53ef\u9006\u505a\u529f\u7684\u5ea6\u89c4\u4e3a<\/span>\uff0c\u53ef\u4ee5\u8bc1\u660e\u8be5\u5ea6\u89c4\u662f\u6b63\u5b9a\u7684\u3002\u6839\u636eCauchy-Schwarz\u4e0d\u7b49\u5f0f\uff0c\u6700\u5c0f\u4e0d\u53ef\u9006\u529f\u662f<\/span>\uff0c\u5176\u4e2d<\/span>\u662f\u4e24\u5e73\u8861\u6001\u95f4\u7684\u8ddd\u79bb\uff0c\u5373\u70ed\u529b\u5b66\u957f\u5ea6\u3002<\/span><\/section>\n

<\/section>\n
\u503c\u5f97\u6307\u51fa\u7684\u662f\uff0c\u70ed\u529b\u5b66\u957f\u5ea6\u5305\u542b\u4e86\u4e00\u4e9b\u52a8\u529b\u5b66\u7684\u53c2\u6570\uff0c\u4f46\u4e0e\u52a8\u529b\u5b66\u8fc7\u7a0b\u65e0\u5173\uff0c\u4e0d\u4f9d\u8d56\u4e8e\u53c2\u6570\u7684\u5177\u4f53\u63a7\u5236\u65b9\u5f0f\u3002\u5728\u8fd9\u4e00\u6570\u5b66\u6846\u67b6\u4e0b\uff0c\u5bfb\u627e\u80fd\u91cf\u6d88\u8017\u6700\u5c0f\u7684\u4f18\u5316\u63a7\u5236\u65b9\u6848\u7b49\u4ef7\u4e8e\u6c42\u89e3\u9ece\u66fc\u51e0\u4f55\u7a7a\u95f4\u4e2d\u7684\u6d4b\u5730\u7ebf\u65b9\u7a0b<\/span> (\u5982\u56fe13\u6240\u793a)<\/span>\u3002\u4e8e\u662f\uff0c\u5c31\u53ef\u4ee5\u5229\u7528\u5fae\u5206\u51e0\u4f55\u5b66\u7684\u65b9\u6cd5\u6c42\u89e3\u70ed\u529b\u5b66\u4e2d\u7684\u6700\u4f18\u63a7\u5236\u95ee\u9898\uff0c\u6bd4\u5982\uff0c\u5229\u7528\u6377\u5f84\u65b9\u6cd5\u4f18\u5316\u5e03\u6717\u70ed\u673a\u7684\u529f\u7387[109]\u3002\u9700\u8981\u63d0\u53ca\u7684\u662f\uff0c\u6700\u8fd1\u4e5f\u6709\u4e00\u4e9b\u7814\u7a76\u4e2d\u5b9a\u4e49\u4e86\u4f9d\u8d56\u4e8e\u65f6\u95f4\u7684\u201c\u5ea6\u89c4\u201d\uff0c\u5f53\u7136\u4e0d\u5177\u6709\u4e25\u683c\u7684\u7a7a\u95f4\u51e0\u4f55\u5c5e\u6027[110]\u3002<\/span><\/section>\n

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\u56fe13  \u80fd\u91cf\u6700\u5c0f\u6d88\u8017\u8def\u5f84\u7684\u51e0\u4f55\u63cf\u8ff0<\/span><\/section>\n<\/section>\n
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\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u8bfb\u4e66\u4f1a\u542f\u52a8\uff01<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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2024\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff0c\u8fd9\u662f\u4e00\u573a\u7edf\u8ba1\u7269\u7406\u5f15\u53d1\u7684\u673a\u5668\u5b66\u4e60\u9769\u547d\u3002\u7edf\u8ba1\u7269\u7406\u5b66\u4e0d\u4ec5\u80fd\u89e3\u91ca\u70ed\u5b66\u73b0\u8c61\uff0c\u8fd8\u80fd\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u4ece\u5fae\u89c2\u7c92\u5b50\u5230\u5b8f\u89c2\u5b87\u5b99\u7684\u5404\u4e2a\u5c42\u7ea7\u5982\u4f55\u8054\u7cfb\u8d77\u6765\uff0c\u590d\u6742\u73b0\u8c61\u5982\u4f55\u6d8c\u73b0\u3002\u5b83\u901a\u8fc7\u7814\u7a76\u5927\u91cf\u7c92\u5b50\u7684\u96c6\u4f53\u884c\u4e3a\uff0c\u6210\u529f\u5730\u5c06\u5fae\u89c2\u4e16\u754c\u7684\u968f\u673a\u6027\u4e0e\u5b8f\u89c2\u4e16\u754c\u7684\u786e\u5b9a\u6027\u8054\u7cfb\u8d77\u6765\uff0c\u4e3a\u6211\u4eec\u7406\u89e3\u81ea\u7136\u754c\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u4e5f\u4e3a\u673a\u5668\u5b66\u4e60\u548c\u4eba\u5de5\u667a\u80fd\u9886\u57df\u7684\u53d1\u5c55\u63d0\u4f9b\u4e86\u91cd\u8981\u63a8\u52a8\u529b\u3002<\/span><\/p>\n


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\u4e3a\u4e86\u6df1\u5165\u63a2\u7d22\u7edf\u8ba1\u7269\u7406\u524d\u6cbf\u8fdb\u5c55\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u897f\u6e56\u5927\u5b66\u7406\u5b66\u9662\u53ca\u4ea4\u53c9\u79d1\u5b66\u4e2d\u5fc3\u8bb2\u5e2d\u6559\u6388\u6c64\u96f7\u7ff0\u3001\u7ebd\u7ea6\u5dde\u7acb\u5927\u5b66\u77f3\u6eaa\u5206\u6821\u5316\u5b66\u548c\u7269\u7406\u5b66\u7cfb\u6559\u6388\u6c6a\u52b2\u3001\u5fb7\u7d2f\u65af\u987f\u7cfb\u7edf\u751f\u7269\u5b66\u4e2d\u5fc3\u535a\u58eb\u540e\u7814\u7a76\u5458\u6881\u5e08\u7fce\u3001\u9999\u6e2f\u6d78\u4f1a\u5927\u5b66\u7269\u7406\u7cfb\u52a9\u7406\u6559\u6388\u5510\u4e7e\u5143\uff0c\u4ee5\u53ca\u591a\u4f4d\u56fd\u5185\u5916\u77e5\u540d\u5b66\u8005\u5171\u540c\u53d1\u8d77\u300c\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u300d\u8bfb\u4e66\u4f1a<\/a>\u3002\u8bfb\u4e66\u4f1a\u65e8\u5728\u63a2\u8ba8\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u6700\u65b0\u7406\u8bba\u7a81\u7834\uff0c\u7edf\u8ba1\u7269\u7406\u5728\u590d\u6742\u7cfb\u7edf\u548c\u751f\u547d\u79d1\u5b66\u4e2d\u7684\u5e94\u7528\uff0c\u4ee5\u53ca\u4e0e\u673a\u5668\u5b66\u4e60\u7b49\u524d\u6cbf\u9886\u57df\u7684\u4ea4\u53c9\u7814\u7a76\u3002\u8bfb\u4e66\u4f1a\u4ece12\u670812\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u56db\u665a20:00-22:00\u8fdb\u884c\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba112\u5468\u3002\u6211\u4eec\u8bda\u631a\u9080\u8bf7\u5404\u4f4d\u670b\u53cb\u53c2\u4e0e\u8ba8\u8bba\u4ea4\u6d41\uff0c\u4e00\u8d77\u63a2\u7d22\u7231\u56e0\u65af\u5766\u773c\u4e2d\u7684\u666e\u9002\u7406\u8bba\uff01<\/span><\/span><\/p>\n


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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>\u4ece\u70ed\u529b\u5b66\u3001\u751f\u547d\u5230\u4eba\u5de5\u667a\u80fd\u7684\u7edf\u8ba1\u7269\u7406\u4e4b\u8def\uff1a\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u8bfb\u4e66\u4f1a\u542f\u52a8\uff01<\/a><\/span><\/p>\n


<\/section>\n<\/section>\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/p>\n

<\/strong><\/section>\n
1. <\/strong>\u7269\u7406\u5b66\u9047\u89c1\u673a\u5668\u5b66\u4e60\uff1a\u6df1\u5ea6\u5b66\u4e60\u7684\u4e0b\u4e00\u4e2a\u7a81\u7834\u53ef\u80fd\u6765\u81ea\u7edf\u8ba1\u7269\u7406\u5b66<\/a><\/strong><\/span><\/section>\n
2. <\/strong>PRL\u901f\u9012\uff1a\u751f\u547d\u7cfb\u7edf\u4e2d\u5bf9\u79f0\u6027\u7834\u7f3a\u7684\u70ed\u529b\u5b66\u9650\u5236<\/a><\/strong><\/span><\/section>\n
3. <\/strong>\u524d\u6cbf\u8fdb\u5c55\uff1a\u5b8f\u89c2\u9ea6\u514b\u65af\u97e6\u5996\u80cc\u540e\u7684\u70ed\u529b\u5b66\u51e0\u4f55\u539f\u7406<\/a><\/strong><\/span><\/section>\n
4. <\/strong><\/span><\/strong>\u65f6\u95f4\u6d4b\u91cf\u53ef\u4ee5\u65e0\u9650\u7cbe\u786e\u5417\uff1f\u5bf9\u65f6\u949f\u7684\u70ed\u529b\u5b66\u65b0\u7406\u89e3<\/a><\/span><\/strong><\/span><\/section>\n
5. <\/strong>\u70ed\u529b\u5b66\u4e0e\u91cf\u5b50\u529b\u5b66\u572821\u4e16\u7eaa\u91cd\u65b0\u76f8\u9047<\/a><\/span><\/strong><\/span><\/strong><\/span><\/section>\n
6. <\/strong>\u56f0\u6270\u70ed\u529b\u5b66\u7684\u4e09\u4e2a\u5996\u7cbe<\/a><\/span><\/strong><\/span><\/strong><\/span><\/section>\n
<\/strong><\/span><\/strong><\/strong><\/span><\/section>\n
7. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong>8.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

9. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n


<\/p>\n


<\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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