{"id":49305,"date":"2024-03-29T16:43:28","date_gmt":"2024-03-29T08:43:28","guid":{"rendered":"https:\/\/swarma.org\/?p=49305"},"modified":"2024-03-29T16:43:28","modified_gmt":"2024-03-29T08:43:28","slug":"%e6%97%b6%e9%97%b4%e4%b8%ba%e4%bd%95%e4%b8%8d%e5%90%8c%e4%ba%8e%e5%85%b6%e4%bb%96%e7%bb%b4%e5%ba%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=49305","title":{"rendered":"\u65f6\u95f4\u4e3a\u4f55\u4e0d\u540c\u4e8e\u5176\u4ed6\u7ef4\u5ea6?"},"content":{"rendered":"
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100\u591a\u5e74\u8fc7\u53bb\u4e86\uff0c<\/span>\uff08\u72ed\u4e49\uff09<\/span>\u76f8\u5bf9\u8bba\u529b\u5b66\u901a\u8fc7\u4e86\u8fc4\u4eca\u4e3a\u6b62\u80fd\u505a\u7684\u3001\u9488\u5bf9\u5b83\u7684\u5b9e\u9a8c\u7684\u68c0\u9a8c\uff0c\u5b83\u7684\u5e94\u7528\u4e5f\u7ed9\u6211\u4eec\u65e5\u5e38\u751f\u6d3b\u5e26\u6765\u5de8\u5927\u5f71\u54cd\u3002\u5b83\u5df2\u66ff\u4ee3\u725b\u987f\u65b9\u7a0b\u6210\u4e3a\u4e00\u4e2a\u666e\u9002\u8fd0\u52a8\u65b9\u7a0b\uff0c\u662f\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u57fa\u7840\u4e4b\u4e00\u30021915\u5e74\uff0c\u7231\u56e0\u65af\u5766\u518d\u6b21\u63a8\u5e7f\u76f8\u5bf9\u6027\u539f\u7406\u4e3a\u5e7f\u4e49\u76f8\u5bf9\u6027\u539f\u7406\uff0c\u628a\u4e07\u6709\u5f15\u529b\u4e5f\u7eb3\u5165\u76f8\u5bf9\u8bba\u529b\u5b66\u7684\u6846\u67b6\u4e2d\uff0c\u8fdb\u4e00\u6b65\u53d1\u5c55\u5bf9\u65f6\u7a7a\u7684\u7406\u8bba\uff0c\u518d\u6b21\u589e\u8fdb\u4e86\u6211\u4eec\u5bf9\u65f6\u7a7a\u7684\u7406\u89e3\u3002\u4ed6\u7528\u9ece\u66fc<\/span>\uff08Riemann\uff09<\/span>\u51e0\u4f55\u66ff\u4ee3\u6b27\u51e0\u91cc\u5fb7\u51e0\u4f55\uff0c\u7528\u5f2f\u66f2\u7684\u65f6\u7a7a\u66ff\u4ee3\u5e73\u76f4\u7684\u65f6\u7a7a\u3002\u6211\u4eec\u6240\u5904\u7684\u65f6\u7a7a\u4e0d\u5355\u4e0d\u662f\u7edd\u5bf9\u6216\u5148\u9a8c\u7684\uff0c\u8fd8\u4f9d\u8d56\u4e8e\u5176\u4e2d\u7684\u7269\u8d28\u8fd0\u52a8\uff0c\u65f6\u7a7a\u53ef\u80fd\u4f1a\u6709\u8d77\u70b9\u3002<\/span><\/span><\/section>\n

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\u4ece\u8ba4\u8bc6\u8bba\u7684\u89d2\u5ea6\uff0c\u9ece\u66fc\u7a7a\u95f4\u7684\u5b58\u5728\u548c\u5e94\u7528\u4e5f\u63d0\u793a\u6211\u4eec\u6b27\u51e0\u91cc\u5fb7\u7a7a\u95f4\u4e0d\u662f\u54f2\u5b66\u610f\u4e49\u4e0b\u5148\u9a8c\u7684\uff0c\u5e7f\u4e49\u76f8\u5bf9\u8bba\u518d\u6b21\u4fc3\u6210\u4e86\u5bf9\u6574\u4e2a\u65f6\u95f4\u3001\u7a7a\u95f4\u89c2\u5ff5\u7684\u53d8\u9769\u3002\u4ece\u7269\u7406\u5b66\u672c\u8eab\u53d1\u5c55\u7684\u89d2\u5ea6\uff0c\u76f8\u5bf9\u8bba\u529b\u5b66\u8fd9\u4e2a\u53d1\u5c55\u7684\u4f8b\u5b50\u544a\u8bc9\u6211\u4eec\u4e00\u4e2a\u6210\u529f\u7684\u65b0\u7269\u7406\u7406\u8bba\u9700\u8981\u5177\u59073\u4e2a\u57fa\u672c\u6761\u4ef6\uff1a\u5305\u62ec\u65e7\u7406\u8bba\u7684\u9002\u7528\u8303\u56f4\uff1b\u9884\u6d4b\u65b0\u5b9e\u9a8c\u5e76\u901a\u8fc7\u5176\u68c0\u9a8c\uff1b\u6709\u5b55\u80b2\u65b0\u601d\u60f3\u3001\u65b0\u6982\u5ff5\u7684\u80fd\u529b\u3002\u53e6\u4e00\u4e2a\u4f17\u6240\u5468\u77e5\u7684\u4f8b\u5b50\u662f\u7ecf\u5178\u529b\u5b66\uff1a\u4f5c\u4e3a\u7a33\u6001\u6781\u9650\uff0c\u5b83\u6210\u529f\u5730\u5438\u6536\u4e86\u9759\u529b\u5b66\u5982\u8457\u540d\u7684\u963f\u57fa\u7c73\u5fb7<\/span>\uff08Archimedes\uff09<\/span>\u6d6e\u529b\u5b9a\u5f8b\u5e76\u5177\u5907\u4e0a\u9762\u8ba8\u8bba\u8fc7\u7684\u5176\u4ed6\u4e24\u4e2a\u57fa\u672c\u6761\u4ef6\u3002<\/span><\/span><\/section>\n

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\u5c3d\u7ba1\u76f8\u5bf9\u8bba\u529b\u5b66\u628a\u65f6\u95f4\u3001\u7a7a\u95f4\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u56db\u7ef4\u65f6\u7a7a\u7ed9\u6211\u4eec\u65f6\u95f4\u7ef4\u5ea6\u3001\u7a7a\u95f4\u7ef4\u5ea6\u7b49\u4ef7\u7684\u60f3\u8c61\uff0c\u4f46\u5b83\u4eec\u4e4b\u95f4\u7684\u53d8\u6362\u4e0d\u50cf\u7a7a\u95f4\u7ef4\u5ea6\u4e4b\u95f4\u7684\u53d8\u6362\u90a3\u6837\u4efb\u610f\u3002\u7c7b\u65f6\u3001\u7c7b\u7a7a\u548c\u7c7b\u5149\u7684\u56db\u7ef4\u65f6\u7a7a\u662f\u76f8\u5bf9\u6027\u4e0d\u53d8\u7684\uff0c\u6211\u4eec\u4e0d\u80fd\u628a\u7c7b\u65f6\u53d8\u6362\u4e3a\u7c7b\u7a7a\u3002\u56db\u7ef4\u65f6\u7a7a\u4e2d\u53d1\u751f\u7684\u4e8b\u4ef6\u4ecd\u7136\u6709\u4e00\u4e2a\u57fa\u672c\u65f6\u5e8f\u3002\u65f6\u95f4\u7ef4\u5ea6\u4e0e\u7a7a\u95f4\u7ef4\u5ea6\u4ecd\u7136\u4e0d\u4e00\u6837\u3002<\/span><\/section>\n


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3. \u91cf\u5b50\u529b\u5b66\u4e2d\u7684\u65f6\u95f4<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u7b2c\u4e8c\u4e2a\u6210\u529f\u7684\u7a81\u7834\u53e3\u7684\u6210\u679c\u662f\u91cf\u5b50<\/span><\/span>\u529b\u5b66[5]\u3002<\/span>\u91cf\u5b50\u529b\u5b66\u57fa\u672c\u4e0a\u8fd8\u662f\u6cbf\u7528\u7ecf\u5178\u529b\u5b66\u7684\u65f6\u95f4\u6982\u5ff5\uff0c\u4f46\u4ece\u4e00\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u89d2\u5ea6\u53d8\u9769\u4e86\u6211\u4eec\u5173\u4e8e\u7a7a\u95f4\u7684\u6982\u5ff5\uff1a\u63cf\u8ff0\u7269\u4f53\u8fd0\u52a8\u7684\u76f8\u7a7a\u95f4\u662f\u6709\u7ed3\u6784\u7684<\/strong>\u3002\u7b80\u5355\u7684\u4f8b\u5b50\u662f\u76f8\u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6ex\u548c\u52a8\u91cfp\u6ee1\u8db3\u4e00\u4e2a\u5bf9\u6613\u5173\u7cfb\uff0c[x, p]=ih\uff0c\u4e0d\u518d\u76f8\u4e92\u72ec\u7acb\uff0c\u5b83\u4eec\u7684\u4e58\u79ef\u4e0d\u80fd\u4ea4\u6362\uff0cxp\u2260px\u3002\u8fd9\u4e2a\u5bf9\u6613\u5173\u7cfb\u4e5f\u662f\u4e00\u5bf9\u5171\u8f6d\u7269\u7406\u91cf\u4e4b\u95f4\u4e0d\u786e\u5b9a\u6027\u5173\u7cfb\u7684\u5178\u578b\u4f8b\u5b50\u3002\u4ece1900\u5e74\u666e\u6717\u514b<\/span>\uff08Planck\uff09<\/span>\u53d1\u73b0\u666e\u9002\u5e38\u6570\u52301925\u5e74\u6d77\u68ee\u5821<\/span>\uff08Heisenberg\uff09<\/span>\u53d1\u73b0\u7b2c\u4e00\u4e2a\u91cf\u5b50\u529b\u5b66\u7684\u8868\u8ff0\u82b1\u4e86\u81f3\u5c11\u4e24\u4ee3\u7269\u7406\u5b66\u5bb6\u56db\u5206\u4e4b\u4e00\u4e16\u7eaa\u7684\u65f6\u95f4\u3002\u6d77\u68ee\u5821\u65b9\u7a0b\u7528\u7b97\u7b26OH<\/sub>\u8868\u793a\u7269\u7406\u91cf\uff0c\u76f4\u63a5\u7528\u4e86\u5bf9\u6613\u5173\u7cfb<\/span>\uff08\u56fe1\uff09<\/span>\u30021926\u5e74\u5efa\u7acb\u7684\u859b\u5b9a\u8c14<\/span>\uff08Schr\u00f6dinger\uff09<\/span>\u65b9\u7a0b\u4e5f\u662f\u5e38\u7528\u7684\u8868\u8ff0\uff0c\u7528\u6ce2\u51fd\u6570\u03c8\u63cf\u8ff0\u7269\u4f53\u7684\u65f6\u7a7a\u72b6\u6001\uff0c\u628a\u76f8\u7a7a\u95f4\u7ed3\u6784\u548c\u5bf9\u6613\u5173\u7cfb\u9690\u542b\u5728\u5176\u4e2d\u3002\u8fd9\u4e24\u79cd\u63cf\u8ff0\u7ed8\u666f\u90fd\u9700\u8981\u9996\u5148\u786e\u5b9a\u7cfb\u7edf\u7684\u54c8\u5bc6\u987f\u91cf\u3002\u5728\u666e\u6717\u514b\u5e38\u6570\u5f88\u5c0f\u7684\u6761\u4ef6\u4e0b\uff0c\u91cf\u5b50\u529b\u5b66\u56de\u5f52\u5230\u7ecf\u5178\u529b\u5b66\u3002<\/span><\/span><\/section>\n

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\u91cf\u5b50\u529b\u5b66\u7acb\u5373\u5728\u4ece\u73bb\u5c14<\/span>\uff08Bohr\uff09<\/span>\u5f00\u59cb\u6c22\u539f\u5b50\u7684\u7406\u8bba\u7814\u7a76\u4e2d\u53d6\u5f97\u6210\u529f\u3002\u4e00\u4e2a\u975e\u5e38\u6210\u529f\u7684\u5e94\u7528\u4f8b\u5b50\u662f\u8d85\u5bfc\u73b0\u8c61\uff1a\u5728\u6211\u4eec\u719f\u77e5\u7684\u4e00\u4e9b\u79d1\u5b66\u5bb6\u5982\u8d39\u66fc<\/span>\uff08Feynman\uff09<\/span>\u3001\u6717\u9053<\/span>\uff08Landau\uff09<\/span>\u7b49\u6ca1\u6709\u53d6\u5f97\u6210\u529f\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u7531\u6559\u6388\u3001\u535a\u58eb\u540e\u3001\u7814\u7a76\u751f\u7ec4\u6210\u7684\u7406\u60f3\u7684\u7814\u7a76\u56e2\u961f\u2014\u2014\u4f46\u76f4\u5230\u4eca\u5929\u5728\u4e13\u5bb6\u8303\u56f4\u5916\u4ecd\u7136\u4e0d\u77e5\u540d\u7684\u56e2\u961f\u57281957\u5e74\u53d1\u73b0\u4e86\u5df4\u4e01-\u5e93\u73c0-\u65bd\u91cc\u5f17<\/span>\uff08Bardeen-Cooper-Schrieffer\uff0cBCS\uff09<\/span>\u5e38\u89c4\u8d85\u5bfc\u7406\u8bba<\/span>\uff08\u5df4\u4e01\u662f\u8fc4\u4eca\u4e3a\u6b62\u552f\u4e00\u5f97\u8fc7\u4e24\u6b21\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7684\u79d1\u5b66\u5bb6\uff09<\/span>\u3002\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6df1\u523b\u7684\u7406\u8bba\uff0c\u5f71\u54cd\u5230\u7269\u7406\u5b66\u5f88\u591a\u9886\u57df\u7684\u53d1\u5c55\uff0c\u5305\u62ec\u57fa\u672c\u7c92\u5b50\u7269\u7406\u7684\u5e0c\u683c\u65af<\/span>\uff08Higgs\uff09<\/span>\u673a\u5236\u3002\u4e0e\u76f8\u5bf9\u8bba\u529b\u5b66\u4e00\u6837\uff0c\u91cf\u5b50\u529b\u5b66\u662f\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u57fa\u7840\u4e4b\u4e00\uff0c\u4e5f\u5bf9\u6211\u4eec\u7684\u65e5\u5e38\u751f\u6d3b\u6709\u5de8\u5927\u5f71\u54cd\uff0c\u8fd9\u662f\u66ff\u4ee3\u7ecf\u5178\u529b\u5b66\u7684\u7b2c\u4e8c\u4e2a\u666e\u9002\u7406\u8bba\u3002<\/span><\/span><\/section>\n

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\u91cf\u5b50\u529b\u5b66\u5bf9\u65f6\u95f4\u3001\u7a7a\u95f4\u8fd8\u5404\u6709\u4e00\u70b9\u91cd\u8981\u7a81\u7834\u3002\u9664\u4e86\u6307\u660e\u76f8\u7a7a\u95f4\u6709\u7ed3\u6784\u4e4b\u5916\uff0c\u91cf\u5b50\u529b\u5b66\u660e\u786e\u8868\u660e\u63cf\u8ff0\u7269\u4f53\u8fd0\u52a8\u7684\u76f8\u7a7a\u95f4\u4e0d\u9650\u4e8e\u6211\u4eec\u5e38\u89c1\u7684\u4e09\u7ef4\u7a7a\u95f4<\/strong><\/span>\uff08\u76f8\u7a7a\u95f4\u662f\u516d\u7ef4\uff09<\/span>\uff0c\u522b\u7684\u7ef4\u5ea6\u4e5f\u4e00\u5b9a\u5b58\u5728\uff0c\u522b\u7684\u7a7a\u95f4\u65b9\u5f0f\u4e5f\u53ef\u7528<\/strong>\u2014\u2014\u6070\u5f53\u7684\u4e00\u822c\u7a7a\u95f4\u662f\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\uff0c\u5b8c\u5168\u8131\u79bb\u7ecf\u5178\u529b\u5b66\u7684\u76f8\u7a7a\u95f4\u3002\u4f8b\u5982\u57fa\u672c\u7c92\u5b50\u5982\u7535\u5b50\u7684\u81ea\u65cb\uff0c\u5fc5\u987b\u4f5c\u4e3a\u72ec\u7acb\u7684\u3001\u989d\u5916\u7684\u81ea\u7531\u5ea6\u63a5\u53d7\u4e0b\u6765\uff0c\u8fd9\u5bf9\u540e\u7eed\u91cf\u5b50\u573a\u8bba\u7684\u53d1\u5c55\u5f71\u54cd\u5de8\u5927\u3002\u5728\u65f6\u95f4\u4e0a\uff0c\u91cf\u5b50\u529b\u5b66\u8868\u660e\u4e00\u5b9a\u7a0b\u5ea6\u7684\u9006\u65f6\u95f4\u8fd0\u52a8\u662f\u53ef\u80fd\u7684<\/strong>\uff0c\u4ece\u5b83\u7684\u8def\u5f84\u79ef\u5206\u8868\u8ff0\u6765\u770b\u5c24\u5176\u660e\u663e\uff1a\u9006\u65f6\u95f4\u8def\u5f84\u6ca1\u6709\u88ab\u6392\u9664\uff0c\u5b83\u7684\u7269\u7406\u540e\u679c\u8fc4\u4eca\u8fd8\u6ca1\u6709\u88ab\u63a2\u7d22\u6e05\u695a\u3002\u91cf\u5b50\u529b\u5b66\u4e0e\u76f8\u5bf9\u8bba\u529b\u5b66\u76f8\u7ed3\u5408\u7684\u72c4\u62c9\u514b<\/span>\uff08Dirac\uff09<\/span>\u65b9\u7a0b\u83b7\u5f97\u77ac\u65f6\u7684\u6210\u529f\u3002\u7ecf\u8fc7\u5404\u81ea\u591a\u5e74\u7684\u51e0\u756a\u52aa\u529b\uff0c\u7535\u78c1\u76f8\u4e92\u4f5c\u7528\u3001\u5f3a\u76f8\u4e92\u4f5c\u7528\u3001\u5f31\u7535\u76f8\u4e92\u4f5c\u7528\u7684\u76f8\u5bf9\u8bba\u91cf\u5b50\u573a\u8bba\u5316\u4e5f\u83b7\u5f97\u6210\u529f\u3002\u7c92\u5b50\u7269\u7406\u7684\u6807\u51c6\u6a21\u578b\uff0c\u7edf\u4e00\u7535\u78c1\u3001\u5f31\u548c\u5f3a\u76f8\u4e92\u4f5c\u7528\u7684\u7406\u8bba\uff0c\u4e5f\u83b7\u5f97\u4e00\u5b9a\u6210\u529f\u3002\u8fd9\u4e9b\u6210\u529f\u7406\u8bba\u7684\u6570\u5b66\u7ed3\u6784\u90fd\u5c5e\u4e8e\u6768\u632f\u5b81\u3001\u7c73\u5c14\u65af<\/span>\uff08Mills\uff09<\/span>\u6240\u53d1\u73b0\u7684\u89c4\u8303\u573a\u3002\u4f46\u662f\uff0c\u4e07\u6709\u5f15\u529b\u6216\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7684\u91cf\u5b50\u5316\uff0c\u8fd8\u6ca1\u6709\u6210\u529f\uff0c\u6709\u5f88\u5f3a\u7684\u7406\u8bba\u77db\u76fe\uff1b\u4ece\u91cf\u5b50\u573a\u8bba\u7684\u89d2\u5ea6\u6765\u5305\u62ec\u5e7f\u4e49\u76f8\u5bf9\u8bba\uff0c\u5982\u8d85\u5f26\u7406\u8bba\uff0c\u4e5f\u8fd8\u6ca1\u6709\u6210\u529f\uff0c\u8fd8\u6ca1\u6709\u4e00\u4e2a\u65b0\u7684\u5b9e\u9a8c\u9a8c\u8bc1\uff0c\u5b83\u4eec\u5728\u56fe1\u4e2d\u7528\u95ee\u53f7\u6807\u8bc6\u3002\u5728\u4e00\u5b9a\u610f\u4e49\u4e0b\u6211\u4eec\u53c8\u56de\u52301905\u5e74\u4e4b\u524d\u7684\u72b6\u6001\uff1a\u5404\u4e2a\u7406\u8bba\u4e4b\u95f4\u8fd8\u4e0d\u5b8c\u5168\u878d\u6d3d\u3002\u8fd9\u8868\u660e\u5b58\u5728\u5f88\u6df1\u523b\u7684\u7406\u8bba\u95ee\u9898\uff0c\u5173\u952e\u5f88\u53ef\u80fd\u662f\u65f6\u95f4\u4e0e\u7a7a\u95f4\u5728\u76f8\u5bf9\u8bba\u4e2d\u548c\u5728\u522b\u7684\u4e00\u822c\u7269\u7406\u7406\u8bba\u5982\u91cf\u5b50\u529b\u5b66\u4e2d\u5230\u5e95\u6709\u4f55\u5dee\u522b\uff0c\u6709\u5f85\u6211\u4eec\u7ee7\u7eed\u63a2\u7d22\u3002<\/span><\/span><\/section>\n
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4. \u6f14\u5316\u529b\u5b66\u4e2d\u7684\u65f6\u95f4<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5c3d\u7ba1\u5b83\u4eec\u7684\u7269\u7406\u5185\u5bb9\u548c\u6570\u5b66\u7ed3\u6784\u5b8c\u5168\u4e0d\u4e00\u6837\uff0c\u91cf\u5b50\u529b\u5b66\u4e0e\u76f8\u5bf9\u8bba\u529b\u5b66\u7684\u8fd0\u52a8\u65b9\u7a0b\u90fd\u6709\u4e00\u4e2a\u4ece\u7ecf\u5178\u529b\u5b66\u5e26\u8fc7\u6765\u7684\u5171\u540c\u6027\u8d28\uff1a\u5bf9\u4e8e\u65f6\u95f4\u53cd\u6f14\u52a8\u529b\u5b66\u662f\u53ef\u9006\u7684\uff0c\u5b64\u7acb\u7cfb\u7edf\u7684\u80fd\u91cf\u662f\u5b88\u6052\u7684\uff0c\u4fe1\u606f\u6216\u71b5\u4e5f\u662f\u5b88\u6052\u7684<\/strong>\u3002\u6709\u65f6\u4eba\u4eec\u4f1a\u88ab\u81ea\u5df1\u624b\u4e2d\u7684\u95ee\u9898\u8bef\u5bfc\uff0c\u4f1a\u5fd8\u6389\u8fd9\u4e2a\u91cd\u8981\u6027\u8d28\uff0c\u8b6c\u5982\u970d\u91d1<\/span>\uff08Hawking\uff09<\/span>\u5c31\u66fe\u7ecf\u5ffd\u89c6\u5b83\u800c\u8f93\u4e86\u5173\u4e8e\u9ed1\u6d1e\u7684\u5b87\u5b99\u4fe1\u606f\u5b88\u6052\u7684\u8d4c\uff0c\u73b0\u5728\u4ed6\u8ba4\u4e3a\u9ed1\u6d1e\u662f\u4f1a\u5e26\u91cf\u5b50\u201c\u8f6f\u6bdb\u201d\u7684\uff0c<\/span><\/span>\u4f1a\u4fdd\u7559\u4fe1\u606f[6]\u3002<\/span>\u4f46\u662f\uff0c\u8fc7\u5ea6\u5f3a\u8c03\u8fd9\u4e2a\u5b88\u6052\u6027\u8d28\u53ef\u80fd\u4f1a\u5bfc\u81f4\u53e6\u4e00\u4e2a\u6781\u7aef\uff0c\u628a\u65f6\u95f4\u4ece\u7269\u7406\u89c4\u5f8b\u7684\u8868\u8ff0\u4e2d\u53d6\u6d88\uff0c\u6ca1\u6709\u65f6\u95f4\u8fd9\u4e2a\u7ef4\u5ea6\uff0c\u4ece\u800c\u628a\u65f6\u95f4\u7684\u5b58\u5728\u770b\u6210\u662f\u4e00\u79cd<\/span><\/span>\u5e7b\u8c61[7]\u3002<\/span>\u8fd9\u4e5f\u662f\u53ef\u4ee5\u7406\u89e3\u7684\uff1a\u5982\u679c\u628a\u80fd\u91cf\u770b\u6210\u201c\u5929\u201d\uff0c\u628a\u4fe1\u606f\u6216\u71b5\u770b\u6210\u201c\u9053\u201d\uff0c\u6211\u4eec\u5df2\u77e5\u4e24\u79cd\u666e\u9002\u52a8\u529b\u5b66\u5bf9\u4e8e\u5b64\u7acb\u7cfb\u7edf\u65e0\u975e\u662f\u8bf4\u201c\u5929\u4e0d\u53d8\u3001\u9053\u4e5f\u4e0d\u53d8\u201d\u3002\u6211\u4eec\u597d\u5947\u7684\u662f\uff0c\u7ecf\u5178\u529b\u5b66\u4ee5\u540e\u662f\u5426\u8fd8\u6709\u522b\u7684\u3001\u4e0d\u5b88\u6052\u7684\u3001\u7b2c3\u79cd\u666e\u9002\u529b\u5b66\u7ed3\u6784\u7684\u53ef\u80fd\uff1f<\/span><\/span><\/section>\n

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\u4e8b\u5b9e\u4e0a\uff0c19\u4e16\u7eaa\u4e2d\u53f6\u51fa\u73b0\u7684\u70ed\u529b\u5b66<\/strong>\u9996\u5148\u5bf9\u8fd9\u4e2a\u95ee\u9898\u63d0\u4f9b\u4e86\u80af\u5b9a\u56de\u7b54\u7684\u53ef\u80fd\u3002\u65e9\u4e8e\u76f8\u5bf9\u8bba\u529b\u5b66\u548c\u91cf\u5b50\u529b\u5b66\u7684\u53d1\u5c55\uff0c\u70ed\u529b\u5b66\u7b2c\u4e8c<\/span>\u5b9a\u5f8b[8]\u660e<\/span>\u786e\u9648\u8ff0\u4e00\u822c\u52a8\u529b\u5b66\u8fc7\u7a0b\u662f\u4e0d\u53ef\u9006\u7684\uff0c\u5b83\u662f\u4eba\u7c7b\u53d1\u73b0\u7684\u666e\u9002\u89c4\u5f8b\u4e4b\u4e00\uff0c\u8fc4\u4eca\u6ca1\u6709\u4efb\u4f55\u5b9e\u9a8c\u3001\u7ecf\u9a8c\u4e0a\u7684\u4f8b\u5916\u3002\u4f46\u662f\uff0c\u70ed\u529b\u5b66\u4e0d\u662f\u771f\u6b63\u7684\u52a8\u529b\u5b66\uff0c\u8fd9\u8ba9\u5b83\u50ac\u751f\u4e86\u4e24\u4e2a\u91cd\u8981\u95ee\u9898\uff1a\u5b83\u7684\u5b58\u5728\u4e0e\u5df2\u77e5\u7684\u666e\u9002\u8fd0\u52a8\u89c4\u5f8b\u76f8\u5bb9\u5417\uff1f\u5982\u679c\u76f8\u5e94\u65b0\u7684\u8fd0\u52a8\u65b9\u7a0b\u5b58\u5728\u7684\u8bdd\uff0c\u4e00\u822c\u5f62\u5f0f\u4f1a\u662f\u4ec0\u4e48\uff1f<\/span><\/section>\n

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\u4ece\u9ea6\u514b\u65af\u97e6\u3001\u73bb\u5c14\u5179\u66fc<\/span>\uff08Boltzmann\uff09<\/span>\u3001\u5409\u5e03\u65af<\/span>\uff08Gibbs\uff09<\/span>\u7b49\u5f00\u59cb\u7684150\u591a\u5e74\u7814\u7a76\u5bf9\u7b2c\u4e00\u4e2a\u95ee\u9898\u7ed9\u51fa\u4e86\u80af\u5b9a\u56de\u7b54\uff1a\u76f8\u5bb9\uff1b\u5e76\u4ea7\u751f\u4e86\u4e00\u95e8\u5bf9\u5e94\u7684\u3001\u5e94\u7528\u8303\u56f4\u4e0e\u70ed\u529b\u5b66\u4e00\u6837\u5e7f\u6cdb\u548c\u6210\u529f\u7684\u5b66\u79d1\u2014\u2014<\/span><\/span>\u7edf\u8ba1\u529b<\/span><\/span>\u5b66<\/span><\/strong>[9]\uff0c<\/span>\u662f\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u4e00\u5757\u91cd\u8981\u57fa\u77f3\u3002\u5bf9\u7b2c\u4e8c\u4e2a\u95ee\u9898\u7684\u56de\u7b54\u6709\u4e24\u4e2a\u76f8\u53cd\u7684\u52aa\u529b\u65b9\u5411\uff1a\u4e0d\u53ef\u9006\u6027\u4ecd\u7136\u7531\u53ef\u9006\u7684\u8fd0\u52a8\u89c4\u5f8b\u4e2d\u4ea7\u751f\uff1b\u6216\u5bfb\u627e\u5168\u65b0\u7684\u7ed3\u6784\u3002\u4ece\u73bb\u5c14\u5179\u66fc\u5f00\u59cb\u7684\u7269\u7406\u5b66\u4e3b\u6d41\u5e0c\u671b\u4e0d\u53ef\u9006\u6027\u80fd\u591f\u4ece\u5df2\u77e5\u7684\u8fd0\u52a8\u89c4\u5f8b\u4ea7\u751f\uff1a\u7ecf\u5178\u529b\u5b66\u548c\u91cf\u5b50\u529b\u5b66\u3002\u5f88\u9057\u61be\uff0c\u8fd9\u79cd\u52aa\u529b\u7ecf\u8fc7150\u591a\u5e74\u8fd8\u6ca1\u6709\u6210\u529f\uff1a\u5e38\u89c1\u7684\u95ee\u9898\u662f\u660e\u786e\u5730\u6216\u9690\u853d\u5730\u603b\u662f\u628a\u4e0d\u53ef\u9006\u6027\u7684\u5047\u8bbe\u5f15\u5165\u5230\u8bba\u8bc1\u8fc7\u7a0b\u4e2d\u3002\u5176\u4f59\u7684\u7814\u7a76\u8981\u4e48\u8bba\u8bc1\u8fc7\u7a0b\u6709\u9519\u3001\u8981\u4e48\u7cfb\u7edf\u592a\u7279\u6b8a\u3002\u4f46\u8fd9\u4e2a\u63a2\u7d22\u5e26\u6765\u4e86\u5f88\u591a\u91cd\u8981\u6210\u679c\uff0c\u52a0\u6df1\u4e86\u6211\u4eec\u5bf9\u8fd0\u52a8\u89c4\u5f8b\u7684\u7406\u89e3\uff0c\u4f8b\u5982\u6df7\u6c8c\u7684\u53d1\u73b0\u4e0e<\/span><\/span>\u7814\u7a76[10]<\/span>\u3002<\/span><\/span><\/section>\n

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\u7b2c\u4e8c\u4e2a\u65b9\u5411\u628a\u7814\u7a76\u8005\u4eec\u5e26\u5230\u5168\u65b0\u7684\u9886\u57df\uff0c\u9047\u5230\u7684\u4e0d\u53ef\u9006\u7684\u8fd0\u52a8\u65b9\u7a0b\u592a\u591a\u4e86\uff0c\u53ef\u7528\u7684\u65b9\u6cd5\u771f\u662f\u201c\u516b\u4ed9\u8fc7\u6d77\uff0c\u5404\u663e\u795e\u901a\u201d\uff0c\u4e00\u822c\u7684\u610f\u89c1\u5bf9\u80fd\u5426\u5f97\u5230\u80af\u5b9a\u7684\u7b54\u6848\u4e00\u76f4\u662f\u4e0d\u786e\u5b9a\u7684\u3002\u8b6c\u5982\u76f4\u5230\u6700\u8fd1<\/span>\uff08\u751a\u81f3\u73b0\u5728\uff09<\/span>\u5f88\u591a\u4eba\u5bf9\u4e00\u822c\u975e\u5e73\u8861\u8fc7\u7a0b\u4e2d\u662f\u5426\u5b58\u5728\u7c7b\u4f3c\u7684\u80fd\u91cf\u51fd\u6570H\u3001\u7edf\u8ba1\u529b\u5b66\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u666e\u9002\u7684\u529b\u5b66\u6846\u67b6\u4ecd\u7136\u6301\u4e00\u4e2a\u6000\u7591<\/span><\/span>\u6001\u5ea6[11]\u3002<\/span>\u5e78\u8fd0\u7684\u662f\uff0c\u7b2c\u4e00\u4e2a\u5bf9\u5e94\u4e8e\u7edf\u8ba1\u529b\u5b66\u6216\u70ed\u529b\u5b66\u7684\u4e00\u822c\u8fd0\u52a8\u65b9\u7a0b\u7ec8\u4e8e\u51fa\u73b0\u4e86\uff0c\u5b83\u7684\u5f62\u5f0f\u4e5f\u975e\u5e38\u201c\u7b80\u5355\u201d<\/span>\uff08\u56fe1\uff09<\/span>\u3002<\/span><\/span><\/section>\n

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\u8fd9\u4e2a\u6f14\u5316\u65b9<\/span>\u7a0b[12]\u5f88<\/span>\u65b0\uff0c\u6211\u56fd\u7269\u7406\u5b66\u5bb6\u5bf9\u5b83\u7684\u5efa\u7acb\u6709\u4e3b\u8981\u8d21\u732e\u3002\u9996\u5148\uff0c\u4e0e\u53e6\u5916\u7684\u57fa\u672c\u529b\u5b66\u7406\u8bba\u7c7b\u4f3c\uff0c\u65b9\u7a0b\u7684\u5f62\u5f0f\u662f\u7406\u8bba\u5047\u8bbe\uff0c\u6f14\u7b97\u7ed3\u679c\u662f\u53ef\u4ee5\u88ab\u5b9e\u9a8c\u68c0\u9a8c\u7684\u3002\u6f14\u5316\u65b9\u7a0b\u662f\u5728\u76f8\u7a7a\u95f4q\u4e2d\u8868\u8ff0\u7684\uff0c\u03b6<\/span>\u662f\u76f8\u7a7a\u95f4\u4e2d\u7684\u968f\u673a\u201c\u529b\u201d\uff0c\u662f\u9ad8\u65af\u767d\u566a\u58f0\uff0c\u5b83\u7684\u5e73\u5747\u503c\u662f\u96f6\uff0c\u3008\u03b6\u3009=0\uff0c<\/sub>\uff0c\u5176\u4e2d:k\u662f\u73bb\u5c14\u5179\u66fc\u5e38\u6570\uff0cT\u662f\u6e29\u5ea6\uff0c\u4e0a\u6807\u03c4\u8868\u793a\u8f6c\u7f6e\uff0c\u03b4(t)\u662f\u72c4\u62c9\u514b\u03b4<\/span>\u51fd\u6570\uff0cD\u662f\u76f8\u7a7a\u95f4\u4e2d\u7684\u6269\u6563\u77e9\u9635\u3002J(q)\u662f\u4e00\u4e2a\u4e00\u822c\u7684\u53cd\u5bf9\u79f0\u77e9\u9635\u3002\u5982\u679c\u7a33\u6001\u6781\u9650\u5b58\u5728\uff0c\u5176\u5206\u5e03\u51fd\u6570\u662f\u6807\u51c6\u7684\u73bb\u5c14\u5179\u66fc-\u5409\u5e03\u65af\u5206\u5e03\u5f62\u5f0f\uff0c<\/sub>\uff0c\u662f\u7edf\u8ba1\u529b\u5b66\u4e2d\u91cd\u8981\u7684\u6b63\u5219\u5206\u5e03\u3002<\/span><\/section>\n

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\u8fd9\u4e2a\u6f14\u5316\u65b9\u7a0b\u663e\u7136\u6ee1\u8db3\u6210\u529f\u7684\u65b0\u7269\u7406\u7406\u8bba\u6240\u9700\u8981\u5177\u5907\u76843\u4e2a\u57fa\u672c\u6761\u4ef6\u4e4b\u4e00\u2014\u2014\u5305\u5bb9\u65e7\u7406\u8bba\u7684\u9002\u7528\u8303\u56f4\u3002\u5f53D=0\uff0c\u5b83\u56de\u5230\u7ecf\u5178\u529b\u5b66\u2014\u2014\u5b64\u7acb\u7cfb\u7edf\u8fd0\u52a8\u7684\u54c8\u5bc6\u987f\u65b9\u7a0b\uff1b\u5b83\u76f4\u63a5\u5bfc\u51fa\u7edf\u8ba1\u529b\u5b66\u7684\u6b63\u5219\u5206\u5e03\uff0c\u4e0d\u9700\u8981\u901a\u5e38\u6559\u79d1\u4e66\u4e2d\u7684\u5927\u7c92\u5b50\u6570<\/span><\/span>\u6761\u4ef6[13]\uff1b\u4e5f<\/span>\u4e0e\u4ece\u5b8c\u5168\u4e0d\u540c\u89c6\u89d2\u5f97\u5230\u7684\u8fd0\u52a8\u65b9\u7a0b<\/span><\/span>\u4e00\u81f4[14]\u3002<\/span>\u53e6\u4e00\u4e2a\u57fa\u672c\u6761\u4ef6\u4e5f\u6ee1\u8db3\u2014\u2014\u5b55\u80b2\u4e86\u65b0\u601d\u60f3\u3001\u65b0\u6982\u5ff5\uff1a\u5b83\u7edf\u4e00\u5e73\u8861\u6001\u548c\u975e\u5e73\u8861\u6001\u8fc7\u7a0b\u7684\u63cf\u8ff0\uff1b\u6307\u51fa\u5b58\u5728\u4e00\u79cd\u5168\u65b0\u7684\u4e0d\u540c\u4e8e\u5e38\u89c1\u4f0a\u85e4<\/span>\uff08Ito\uff09<\/span>\u548c\u65af\u5353\u59a5\u8bfa\u7ef4\u5947<\/span>\uff08Stratonovich\uff09<\/span>\u79ef\u5206\u7684\u968f\u673a<\/span><\/span>\u79ef\u5206[15]\uff0c<\/span>\u5bf9\u5e94\u7684\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u81ea\u53d1\u73b0\u4ee5\u6765\u4e0d\u505c\u5730\u5728<\/span><\/span>\u88ab\u7814\u7a76[16-19]\u3002<\/span>\u4ece\u6f14\u5316\u529b\u5b66\u7528\u6781\u9650(D=0)\u5305\u5bb9\u7ecf\u5178\u529b\u5b66\u7684\u4f8b\u5b50\u4e2d\u770b\u5230\uff0c\u968f\u673a\u529b\u7684\u8d77\u6e90\u662f\u7cfb\u7edf\u7684\u5f00\u653e\u6027\uff1a\u7cfb\u7edf\u4e4b\u5916\u7684\u3001\u522b\u7684\u81ea\u7531\u5ea6\u5b58\u5728\uff0c\u5b83\u4eec\u7684\u5f71\u54cd\u5bfc\u81f4\u968f\u673a\u529b\uff0c\u4e00\u822c\u6765\u8bf4\u968f\u673a\u529b\u542b\u6709\u7cfb\u7edf\u529b\u5b66\u91cf\u6216\u76f8\u7a7a\u95f4\u7684\u53d8\u91cf\uff0c\u5177\u4f53\u5f62<\/span><\/span>\u5f0f\u5fc5\u987b\u7531\u5177\u4f53\u95ee\u9898\u51b3\u5b9a\u3002\u6f14\u5316\u65b9\u7a0b\u7684\u5f88\u591a\u7279\u6b8a\u4f8b\u5b50\u5df2\u7ecf\u88ab\u5f88\u591a\u7814\u7a76\u8005\u53d1\u73b0[14]\uff0c<\/span>\u4f46\u5bf9\u5176\u9690\u542b\u7684\u666e\u9002\u6027\u8ba4\u8bc6\u4e0d\u8db3\uff0c\u76ee\u524d\u4e3a\u6b62\u7684\u4e3b\u6d41\u8ba4\u4e3a\u5e94\u8be5\u4ece\u5b88\u6052\u7684\u8fd0\u52a8\u65b9\u7a0b\u5bfc\u51fa\uff0c\u5ffd\u89c6\u4e86\u8fd9\u79cd\u63a8\u5bfc\u9700\u8981\u4e00\u7ec4\u5168\u65b0\u7684\u989d\u5916\u5047<\/span><\/span>\u8bbe[13]<\/span>\u3002<\/span><\/span><\/section>\n

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\u968f\u673a\u201c\u529b\u201d\u03b6\u4e0e\u6269\u6563\u77e9\u9635D\u7684\u5173\u7cfb\u662f\u7edf\u8ba1\u7269\u7406\u4e2d\u8457\u540d\u7684\u8017\u6563-\u6da8\u843d\u5173\u7cfb\u7684\u4e00\u4e2a\u7279\u4f8b\uff0c\u4f46\u5728\u6f14\u5316\u529b\u5b66\u7684\u8868\u8ff0\u4e2d\u662f\u4f5c\u4e3a\u5b9a\u4e49\u51fa\u73b0\u7684\uff0c\u53ef\u79f0\u4e3a\u201cF\u5b9a\u7406\u201d\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u5728\u6f14\u5316\u529b\u5b66\u4e2d\u666e\u904d\u6210\u7acb\uff0c\u5b9e\u9a8c\u4e0a\u662f\u53ef\u4ee5\u68c0\u9a8c\u7684\u3002\u8fd9\u4e2a\u5b9a\u4e49\u53ef\u4ee5\u770b\u6210\u725b\u987f\u7b2c\u4e09\u5b9a\u5f8b\u7684\u4e00\u4e2a\u63a8\u5e7f\uff1a\u7269\u7406\u4f53\u7cfb\u5982\u4f55\u4e0e\u672a\u77e5\u7684\u4e16\u754c\u76f8\u4e92\u4f5c\u7528\u3002\u66f4\u8fdb\u4e00\u6b65\u7684\u7814\u7a76\u53d1\u73b0\u7cfb\u7edf\u7684\u6269\u6563\u77e9\u9635\u548c\u6469\u64e6\u77e9\u9635\u8fd8\u5e94\u8be5\u6ee1\u8db3\u4e00\u4e2a\u666e\u9002\u7684\u5173<\/span>\u7cfb[12]\uff0c<\/span>\u7231\u56e0\u65af\u5766\u5173\u7cfb\u2014\u2014\u6469\u64e6\u7cfb\u6570\u4e0e\u6269\u6563\u7cfb\u6570\u4e58\u79ef\u662f\u5e38\u6570\u2014\u2014\u5728\u9ad8\u7ef4\u3001\u975e\u7ebf\u6027\u3001\u65e0\u7ec6\u81f4\u5e73\u8861\u60c5\u51b5\u4e0b\u7684\u63a8\u5e7f\uff0c\u662f\u4e00\u4e2a\u65b0\u7684\u9884\u6d4b\uff0c\u4e5f\u80fd\u88ab\u5b9e\u9a8c\u68c0\u9a8c\u3002<\/span><\/section>\n

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\u6f14\u5316\u529b\u5b66\u9884\u6d4b\u4e86\u4e00\u7cfb\u5217\u968f\u673a\u52a8\u529b\u5b66\u7b49\u5f0f\uff0c\u5176\u4e2d\u4e00\u90e8\u5206\u662f\u719f\u77e5\u7684\u70ed\u529b\u5b66\u4e0d\u7b49\u5f0f\u7684\u63a8\u5e7f\uff0c\u53ef\u7531\u5b9e\u9a8c<\/span>\u68c0\u9a8c[12]\u3002\u5b83<\/span>\u4e5f\u6307\u51fa\u76ee\u524d\u57fa\u4e8e\u5e73\u5747\u573a\u610f\u4e49\u4e0b\u7684\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u4f1a\u5728\u6da8\u843d\u5927\u7684\u60c5\u51b5\u4e0b\u51fa\u73b0\u4e0e\u5b9e\u9a8c\u7684\u504f\u5dee\uff0c\u5e94\u8be5\u91cd\u65b0\u68c0\u9a8c\u5176\u9648\u8ff0\u3002\u6f14\u5316\u65b9\u7a0b\u6240\u4f9d\u8d56\u7684\u65b0\u7684\u968f\u673a\u79ef<\/span>\u5206[14]\u5728<\/span>\u7269\u7406\u7cfb\u7edf\u4e2d\u4e5f\u662f\u53ef\u4ee5\u68c0\u9a8c\u7684\uff0c\u610f\u4e49\u7c7b\u4f3c\u4e8e\u5e7f\u4e49\u76f8\u5bf9\u8bba\u4e2d\u7a7a\u95f4\u662f\u5426\u5f2f\u66f2\u3002\u6210\u529f\u7684\u65b0\u7269\u7406\u7406\u8bba\u6240\u9700\u8981\u5177\u5907\u76843\u4e2a\u57fa\u672c\u6761\u4ef6\u6f14\u5316\u529b\u5b66\u90fd\u80fd\u6ee1\u8db3\u3002\u6570\u5b66\u4e0a\uff0c\u6f14\u5316\u529b\u5b66\u662f\u57fa\u4e8e\u65b0\u53d1\u73b0\u7684\u4e00\u4e2a\u5f3a\u6709\u529b\u7684\u6570\u5b66<\/span>\u7ed3\u6784[16, 19]\uff1a<\/span>\u4e00\u4e2a\u968f\u673a\u8fc7\u7a0b\u4e2d\u603b\u5b58\u5728\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u7269\u7406\u4e2d\u80fd\u91cf\u7684\u51fd\u6570\uff0c\u8bb0\u4e3aH\uff0c\u52a8\u529b\u5b66\u8fc7\u7a0b\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u90e8\u5206\uff1a\u4fdd\u6301H\u4e0d\u53d8\u7684\u90e8\u5206\uff0c\u8bb0\u4e3aJ\u8ba9H\u51cf\u5c11\u7684\u90e8\u5206\uff0c\u8bb0\u4e3aD\uff0c\u7531\u968f\u673a\u9879\u7684\u65b9\u5dee\u786e\u5b9a\u3002\u6f14\u5316\u529b\u5b66\u53ef\u4ee5\u4f5c\u4e3a\u7b2c3\u4e2a\u666e\u9002\u529b\u5b66\uff0c\u662f\u73b0\u4ee3\u7269\u7406\u5b66\u7684\u53e6\u4e00\u57fa\u7840\u3002<\/span><\/section>\n

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\u6f14\u5316\u529b\u5b66\u63d0\u4f9b\u4e86\u63cf\u8ff0\u975e\u5e73\u8861\u6001\u8fc7\u7a0b\u7684\u4e00\u822c\u6846\u67b6\uff0c\u5b83\u7684\u7a33\u6001\u6781\u9650\u2014\u2014\u7edf\u8ba1\u529b\u5b66\u662f\u76ee\u524d\u5e94\u7528\u5e7f\u8303\u3001\u6210\u529f\u7684\u7269\u7406<\/span>\u7406\u8bba[20]\u3002\u4e0d<\/span>\u4f46\u6210\u529f\u5730\u8fd0\u7528\u5728\u5b8f\u89c2\u4e16\u754c\uff0c\u800c\u4e14\u4e5f\u6210\u529f\u5730\u8fd0\u7528\u5728\u91cf\u5b50\u573a\u8bba\u63cf\u8ff0\u7684\u5fae\u89c2\u4e16\u754c\u548c\u5e7f\u4e49\u76f8\u5bf9\u8bba\u8868\u8ff0\u7684\u5b87\u89c2\u4e16\u754c\u3002\u6f14\u5316\u529b\u5b66\u4ee5\u4e00\u79cd\u5b8c\u5168\u4e0d\u540c\u4e8e\u91cf\u5b50\u529b\u5b66\u7684\u65b9\u5f0f\u5f15\u5165\u4e0d\u786e\u5b9a\u6027\uff0c\u5047\u8bbe\u7269\u7406\u4f53\u7cfb\u662f\u5f00\u653e\u7684\u3001\u5b9e\u9645\u8fc7\u7a0b\u603b\u662f\u4e0d\u53ef\u9006\u7684\u3002\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\u4e0d\u786e\u5b9a\u6027\u662f\u5173\u4e8e\u76f8\u7a7a\u95f4\u6216\u5171\u8f6d\u7269\u7406\u91cf\u7684\uff0c\u800c\u8fd0\u52a8\u8fc7\u7a0b\u662f\u53ef\u9006\u7684\u3002\u6f14\u5316\u529b\u5b66\u4e2d\u7684\u53ef\u9006\u6027\u7c7b\u4f3c\u4e8e\u79d1\u5b66\u7684\u91cd\u8981\u57fa\u77f3\u4e4b\u4e00\u2014\u2014\u6d4b\u91cf\uff0c\u6d4b\u91cf\u8fc7\u7a0b\u662f\u4e0d\u53ef\u9006\u7684\u3002\u5728\u7ecf\u5178\u529b\u5b66\u4e2d\u6d4b\u91cf\u5bf9\u7cfb\u7edf\u7684\u5f71\u54cd\u5728\u7406\u8bba\u4e0a\u53ef\u4ee5\u65e0\u9650\u5730\u5c0f\u4ee5\u81f3\u4e8e\u80fd\u88ab\u5ffd\u7565\u4e0d\u8ba1\uff0c\u800c\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\u6d4b\u91cf\u6709\u5c0f\u5355\u4f4d\uff0c~h<\/em> In2\uff0c\u666e\u6717\u514b\u5e38\u6570\u548c\u6bd4\u7279\u3002\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u6f14\u5316\u529b\u5b66\u4f1a\u5bf9\u89e3\u51b3\u91cf\u5b50\u529b\u5b66\u4e2d\u7684\u6d4b\u91cf\u95ee\u9898\u2014\u2014\u73bb\u5c14\u548c\u7231\u56e0\u65af\u5766\u7ec8\u751f\u8ba8\u8bba\u4f46\u6ca1\u6709\u83b7\u5f97\u5171\u8bc6\u7684\u95ee\u9898\u63d0\u4f9b\u4e00\u4e2a\u91cd\u65b0\u8003\u8651\u7684\u601d\u8def\u3002<\/span><\/section>\n

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\u6b64\u5916\u8fd8\u6709\u4e00\u7cfb\u5217\u7684\u4e0e\u65f6\u95f4\u76f8\u5173\u7684\u95ee\u9898\u9700\u8981\u56de\u7b54\uff0c\u96be\u5ea6\u4e5f\u8bb8\u8981\u5c0f\u4e00\u70b9\uff1a\u6211\u4eec\u6ce8\u610f\u5230\u76f8\u5bf9\u8bba\u91cf\u5b50\u573a\u8bba\u662f\u76f8\u5bf9\u8bba\u529b\u5b66\u4e0e\u91cf\u5b50\u529b\u5b66\u7684\u4f18\u7f8e\u7ed3\u5408\uff0c\u4f46\u5b83\u8fde\u63a5\u5230\u6f14\u5316\u529b\u5b66\u6216\u7edf\u8ba1\u529b\u5b66\u5c31\u663e\u5f97\u7279\u8bbe\u6027\u5f88\u5f3a\uff0c\u76ee\u524d\u597d\u7684\u505a\u6cd5\u4e4b\u4e00\u662f\u4e45\u4fdd-\u9a6c\u4e01-\u65bd\u6e29\u683c<\/span>\uff08Kubo-Martin-Schwinger\uff09<\/span>\u6761\u4ef6\uff0c\u5728\u7406\u8bba\u4e0a\u8fd8\u53ef\u4ee5\u6bd4\u8fd9\u4e2a\u6761\u4ef6\u505a\u5f97\u66f4\u597d\u5417\uff1f\u8d85\u5f26\u7406\u8bba\u4e2d\u7684\u591a\u5b87\u5b99\u7406\u8bba\u5df2\u7ecf\u5728\u5e94\u7528\u6f14\u5316\u7406\u8bba\uff0c\u540e\u8005\u7684\u89d2\u8272\u53ef\u4ee5\u66f4\u5927\u5417\uff1f\u6211\u4eec\u80fd\u628a3\u79cd\u666e\u9002\u529b\u5b66\u90fd\u7edf\u4e00\u5728\u4e00\u4e2a\u7406\u8bba\u6784\u67b6\u4e2d\u5417\uff1f\u8fd9\u4e2a\u7edf\u4e00\u662f\u4f1a\u5728\u7edf\u4e00\u56db\u79cd\u76f8\u4e92\u4f5c\u7528\u4e4b\u524d\u8fd8\u662f\u4e4b\u540e\uff1f\u6211\u4eec\u7684\u5b87\u5b99\u5230\u5e95\u662f\u5b64\u7acb\u7684\u8fd8\u662f\u5f00\u653e\u7684\uff1f\u7b49\u7b49\u3002\u5bf9\u6709\u5fd7\u63a2\u7d22\u7684\u4eba\u4eec\uff0c\u4e5f\u8bb8\u7b2c\u4e00\u6b65\u662f\u4e86\u89e3\u7269\u7406\u5b66\u5df2\u7ecf\u53d6\u5f97\u7684\u3001\u6bd4\u8f83\u786e\u5b9a\u7684<\/span><\/span>\u6210\u5c31[21]\u3002<\/span>\u7136\u540e\uff0c\u4f53\u9a8c\u3001\u4eab\u53d7\u4f60\u7684\u63a2\u7d22\u5386\u7a0b\u3002\u6216\u8005\uff0c\u7eaf\u7cb9\u6765\u6b23\u8d4f\u4eba\u7c7b\u7406\u89e3\u65f6\u95f4\u8fd9\u4e00\u8270\u82e6\u5353\u7edd\u7684\u594b\u6597\u3002<\/span><\/span><\/section>\n

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[2]<\/span> Newton I. The Principia: Mathematical Principles of Natural Philosophy. New York: University of California Press, 1999 [Newton I. \u8d75\u632f\u6c5f, \u8bd1. \u81ea\u7136\u54f2\u5b66\u7684\u6570\u5b66\u539f\u7406. \u5317\u4eac: \u5546\u52a1\u5370\u4e66\u9986, 2006]<\/span><\/section>\n
[3]<\/span> Peng H W, Xu X S. Introduction to Theoretical Physics (in Chinese). Beijing: Peking University Press, 1998 [\u5f6d\u6853\u6b66, \u5f90\u9521\u7533. \u7406\u8bba\u7269\u7406\u57fa\u7840. \u5317\u4eac: \u5317\u4eac\u5927\u5b66\u51fa\u7248\u793e, 1998]<\/span><\/section>\n
[4]<\/span> Zhang Y Z. Experimental Foundation of Special Relativity (in Chinese). Beijing: Science Press, 1979 [\u5f20\u5143\u4ef2. \u72ed\u4e49\u76f8\u5bf9\u8bba\u5b9e\u9a8c\u57fa\u7840. \u5317\u4eac: \u79d1\u5b66\u51fa\u7248\u793e, 1979]<\/span><\/section>\n
[5]<\/span> Wang Z X. Principle of Quantum Mechanics (in Chinese). 2nd ed.. Beijing: Peking University Press, 2008 [\u738b\u6b63\u884c. \u91cf\u5b50\u529b\u5b66\u539f\u7406. \u7b2c 2 \u7248. \u5317\u4eac: \u5317\u4eac\u5927\u5b66\u51fa\u7248\u793e, 2008]<\/span><\/section>\n
[6]<\/span><\/span> Hawking J W, Perry M J, Strominger A. Black holes have soft quantum hair. Phys Rev Lett, 2016, 116: 231301<\/span><\/section>\n
[7]<\/span><\/span> Barbour J. The End of Time. New York: Oxford University Press, 2000<\/span><\/section>\n
[8]<\/span> Wang Z X. Thermodynamics (in Chinese). 2nd ed. Beijing: Peking University Press, 2014 [\u738b\u7af9\u6eaa. \u70ed\u529b\u5b66. \u7b2c 2 \u7248. \u5317\u4eac: \u5317\u4eac\u5927\u5b66\u51fa\u7248\u793e, 2014]<\/span><\/section>\n
[9]<\/span> Gibbs J W. Elementary Principles in Statistical Mechanics. New York: Charles Scribner\u2019s Sons, 1902 [Gibbs J W. \u6bdb\u4fca\u96ef, \u8bd1. \u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406. \u5408\u80a5: \u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\u51fa\u7248\u793e, 2016]<\/span><\/section>\n
[10]<\/span> Hao B L. Directions in Chaos (1&2). Singapore: World Scientific, 1987, 1988<\/span><\/section>\n
[11]<\/span> Lu X Y, Lin J Z. Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials (in Chinese)? Chin Sci Bull, 2017, 62: 1115\u20131118 [\u9646\u5915\u4e91, \u6797\u5efa\u5fe0. \u80fd\u5426\u53d1\u5c55\u5173\u4e8e\u6e4d\u6d41\u52a8\u529b\u5b66\u548c\u9897\u7c92\u6750\u6599\u8fd0\u52a8\u5b66\u7684\u7efc\u5408\u7406\u8bba? \u79d1\u5b66\u901a\u62a5, 2017, 62: 1115\u20131118]<\/span><\/section>\n
[12]<\/span> Ao P. Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics. Commun Theor Phys, 2008, 49: 1073\u20131090<\/span><\/section>\n
[13]<\/span> Ao P. From N=\u221e to N=1: Arrival of dynamical foundation for statistical mechanics (in Chinese). In: TD Lee Library, ed. Essays in Honor of the 90th Birthday of TD Lee. Shanghai: Shanghai Jiao Tong University Press, 2016. 281\u2013287 [\u6556\u5e73. \u4ece N=\u221e\u5230 N=1: \u671f\u671b\u5df2\u4e45\u7684\u7edf\u8ba1\u529b\u5b66\u666e\u9002\u52a8\u529b\u5b66\u57fa\u7840\u5df2\u5230\u6765. \u674e\u653f\u9053\u56fe\u4e66\u9986, \u7f16. \u5fc3\u901a\u5929\u5b87\u2014\u2014\u674e\u653f\u9053\u6559\u6388\u4e5d\u5341\u534e\u8bde\u6587\u96c6. \u4e0a\u6d77: \u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u51fa\u7248\u793e, 2016. 281\u2013287]<\/span><\/section>\n
[14]<\/span> Ao P, Kwon C, Qian H. On the existence of potential landscape in the evolution of complex systems. Complexity, 2007, 12: 19\u201327<\/span><\/section>\n
[15]<\/span> Qian H, Ao P, Tu Y, et al. A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales. Chem Phys Lett, 2016, 665: 153\u2013161<\/span><\/section>\n
[16]<\/span> Ao P. Potential in stochastic differential equations: Novel construction. J Phys A, 2004, 37: L25\u2013L30<\/span><\/section>\n
[17] <\/span>Kwon C, Ao P, Thouless D J. Structure of stochastic dynamics near fixed points. Proc Natl Acad Sci USA, 2005, 102: 13029\u201313033<\/span><\/section>\n
[18]<\/span> Ma Y A, Tan Q J, Yuan R S, et al. Potential function in a continuous dissipative chaotic system: Decomposition scheme and role of strange attractor. Int J Bifurc Chaos, 2014, 24: 1450015<\/span><\/section>\n
[19]<\/span> Yuan R, Tang Y, Ao P. SDE decomposition and A-type stochastic interpretation in nonequilibrium processes. Front Phys, 2017, 12: 120201<\/span><\/section>\n
[20]<\/span><\/span> Ao P. The work of David J Thouless: The discovery of topological phase transition led by curiosity (in Chinese). Chin Sci Bull, 2017, 62: 1199\u20131203 [\u6556\u5e73. \u5927\u536b \u90b5\u52d2\u65af\u7684\u6cbb\u5b66\u548c\u5efa\u6811: \u7eaf\u7cb9\u63a2\u7d22\u51cc\u7edd\u9876. \u79d1\u5b66\u901a\u62a5, 2017, 62: 1199\u20131203]<\/span><\/section>\n
[21]<\/span> Brown L M, Pais A, Pippard B. Twentieth Century Physics (I-III). New York: CRC Press, 1995 [Brown L M, Pais A, Pippard B. \u5218\u5bc4\u661f, \u8bd1. \u4e8c\u5341\u4e16\u7eaa\u7269\u7406\u5b66(1\u20133). \u5317\u4eac: \u79d1\u5b66\u51fa\u7248\u793e, 2014]<\/span><\/section>\n


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\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n


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\u4f5c\u8005\u7b80\u4ecb\uff1a<\/span><\/section>\n
\u6556\u5e73\uff08\u56db\u5ddd\u5927\u5b66\u751f\u7269\u533b\u5b66\u5de5\u7a0b\u5b66\u9662\u6559\u6388\uff0c\u6559\u80b2\u90e8\u957f\u6c5f\u5b66\u8005\u5956\u52b1\u8ba1\u5212\u7279\u8058\u6559\u6388\uff09<\/span><\/section>\n
\u672c\u6587\u539f\u6587\u53d1\u8868\u4e8e\u300a\u79d1\u5b66\u901a\u62a5\u300b2018\u5e74\u7b2c2\u671f\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60\u8bfb\u4e66\u4f1a\u542f\u52a8<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u81ea\u7531\u80fd\u539f\u7406\u88ab\u8ba4\u4e3a\u662f\u201c\u81ea\u8fbe\u5c14\u6587\u81ea\u7136\u9009\u62e9\u7406\u8bba\u540e\u6700\u5305\u7f57\u4e07\u8c61\u7684\u601d\u60f3\u201d\uff0c\u5b83\u8bd5\u56fe\u4ece\u7269\u7406\u3001\u751f\u7269\u548c\u5fc3\u667a\u7684\u89d2\u5ea6\u63d0\u4f9b\u667a\u80fd\u4f53\u611f\u77e5\u548c\u884c\u52a8\u7684\u7edf\u4e00\u6027\u89c4\u5f8b\uff0c\u4ece\u7b2c\u4e00\u6027\u539f\u7406\u51fa\u53d1\u89e3\u91ca\u667a\u80fd\u4f53\u66f4\u65b0\u8ba4\u77e5\u3001\u63a2\u7d22\u548c\u6539\u53d8\u4e16\u754c\u7684\u673a\u5236\uff0c\u4ece\u800c\u5bf9\u4eba\u5de5\u667a\u80fd\uff0c\u7279\u522b\u662f\u5f3a\u5316\u5b66\u4e60\u4e16\u754c\u6a21\u578b\u3001\u901a\u7528\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u5177\u6709\u91cd\u8981\u542f\u53d1\u610f\u4e49\u3002<\/span><\/section>\n


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\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u535a\u58eb\u751f\u725f\u7267\u4e91\uff0c\u5357\u4eac\u822a\u7a7a\u822a\u5929\u5927\u5b66\u526f\u6559\u6388\u4f55\u771f\uff0c\u4ee5\u53ca\u9aa5\u667a\u667a\u80fd\u79d1\u6280\u7b97\u6cd5\u5de5\u7a0b\u5e08\u3001\u516c\u4f17\u53f7 CreateAMind \u4e3b\u7f16\u5f20\u5fb7\u7965\uff0c\u5171\u540c\u53d1\u8d77\u300c\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60\u8bfb\u4e66\u4f1a\u300d\uff0c\u5e0c\u671b\u63a2\u8ba8\u81ea\u7531\u80fd\u539f\u7406\u3001\u5f3a\u5316\u5b66\u4e60\u4e16\u754c\u6a21\u578b\uff0c\u4ee5\u53ca\u8111\u4e0e\u610f\u8bc6\u95ee\u9898\u4e2d\u7684\u9884\u6d4b\u52a0\u5de5\u7406\u8bba\u7b49\u524d\u6cbf\u4ea4\u53c9\u95ee\u9898\uff0c\u63a2\u7d22\u8fd9\u4e9b\u4e0d\u540c\u9886\u57df\u80cc\u540e\u8574\u542b\u7684\u611f\u77e5\u548c\u884c\u52a8\u7684\u7edf\u4e00\u539f\u7406\u3002\u8bfb\u4e66\u4f1a\u4ece3\u670810\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u65e5\u4e0a\u534810:00-12:00\uff0c\u6301\u7eed\u65f6\u95f4\u9884\u8ba18-10\u5468\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff01<\/span><\/p>\n


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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n
\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1a\u63a2\u7d22\u611f\u77e5\u548c\u884c\u52a8\u7684\u7edf\u4e00\u539f\u7406<\/a><\/span><\/section>\n

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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
1. <\/strong>\u70ed\u529b\u5b66\u5982\u4f55\u89e3\u91ca\u8fdb\u5316\u8bba\uff1a\u6700\u5927\u5316\u71b5\u4ea7\u751f\u539f\u7406\u9a71\u52a8\u4e0b\u7684\u81ea\u7136\u9009\u62e9<\/a><\/strong><\/span><\/strong><\/section>\n
2. <\/strong>\u70ed\u529b\u5b66\u600e\u6837\u7406\u89e3\u751f\u547d\uff1a\u71b5\u3001\u4fe1\u606f\u3001\u81ea\u7531\u80fd\u548c\u590d\u6742\u6027\u7684\u6a21\u7cca\u56fe\u666f<\/a><\/strong><\/span><\/strong><\/section>\n
3.<\/strong> \u7b2c\u4e09\u6b21\u79d1\u5b66\u8303\u5f0f\u8f6c\u79fb\uff1f<\/a><\/a><\/strong><\/span><\/section>\n
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4. <\/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><\/strong>5.<\/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><\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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

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