{"id":50833,"date":"2024-06-10T23:06:01","date_gmt":"2024-06-10T15:06:01","guid":{"rendered":"https:\/\/swarma.org\/?p=50833"},"modified":"2024-06-10T23:06:01","modified_gmt":"2024-06-10T15:06:01","slug":"%e8%be%be%e5%b0%94%e6%96%87%e5%8a%9b%e5%ad%a6-%e7%94%9f%e5%91%bd%e7%9a%84%e5%8a%9b%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=50833","title":{"rendered":"\u8fbe\u5c14\u6587\u529b\u5b66\u2014\u2014\u751f\u547d\u7684\u529b\u5b66"},"content":{"rendered":"
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1950\u5e74\u4ee3\u521d\uff0c\u674e\u653f\u9053\u5148\u751f\u548c\u6768\u632f\u5b81\u5148\u751f\u5728\u7269\u6001\u76f8\u53d8\u7684\u7edf\u8ba1\u529b\u5b66\u57fa\u7840\u9886\u57df\u505a\u51fa\u6839\u672c\u6027\u7684\u8d21\u732e\u3002\u4ed6\u4eec\u8003\u5bdf\u7cfb\u7edf\u5f88\u5927<\/span>\uff08\u5373N\u2192\u221e\uff09<\/span>\u65f6\u7684\u884c\u4e3a [1]\u3002\u7edf\u8ba1\u529b\u5b66\u548c\u70ed\u529b\u5b66\u7684\u5de8\u5927\u6210\u529f\u518d\u6b21\u5f15\u51fa\u4e00\u4e2a\u4ece\u73bb\u5c14\u5179\u66fc\u65f6\u4ee3\u5c31\u6709\u7684\u57fa\u672c\u95ee\u9898\uff1a\u7edf\u8ba1\u529b\u5b66\u6709\u81ea\u5df1\u7684\u52a8\u529b\u5b66\u57fa\u7840\u5417\uff1f<\/strong>\u73bb\u5c14\u5179\u66fc<\/span>\uff08L. Boltzmann\uff09<\/span>\u7ed9\u51fa\u8fc7\u51e0\u79cd\u5c1d\u8bd5\u7b54\u6848\uff0c\u4f46\u6ca1\u6709\u4e00\u4e2a\u662f\u666e\u9002\u7684\u3002\u4f8b\u5982\uff0c\u5176\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u65b9\u7a0b<\/span>\uff08\u73b0\u5728\u79f0\u4e3a\u73bb\u5c14\u5179\u66fc\u65b9\u7a0b\uff09<\/span>\u660e\u663e\u53ea\u9002\u7528\u4e8e\u4e00\u7c7b\u7279\u6b8a\u7cfb\u7edf\u3002\u73bb\u5c14\u5179\u66fc\u7684\u4e0d\u6210\u529f\u5bfc\u81f4\u4e86\u4e24\u79cd\u5178\u578b\u4f46\u5b8c\u5168\u4e0d\u540c\u7684\u52aa\u529b\u65b9\u5411\uff1a<\/span>\u4e00\u90e8\u5206\u7269\u7406\u5b66\u5bb6\u8ba4\u4e3a\u5df2\u6709\u7684\u57fa\u672c\u666e\u9002\u52a8\u529b\u5b66<\/span>\uff08\u5982\u91cf\u5b50\u529b\u5b66\uff09<\/span>\u5305\u542b\u4e86\u70ed\u529b\u5b66\uff0c\u5173\u952e\u5728\u4e8e\u5982\u4f55\u627e\u5230\u6070\u5f53\u7684\u65b9\u6848\uff1b<\/span>\u53e6\u4e00\u90e8\u5206\u7269\u7406\u5b66\u5bb6\u8ba4\u4e3a\uff0c\u70ed\u529b\u5b66\u4e0d\u5305\u542b\u4e8e\u91cf\u5b50\u529b\u5b66\uff0c\u5fc5\u987b\u5f15\u5165\u7279\u8bbe\u6027\u5047\u8bbe\u3002\u6b64\u5916\uff0c\u4ece\u73bb\u5c14\u5179\u66fc\u5f00\u59cb\uff0c\u5bf9\u7edf\u8ba1\u529b\u5b66\u548c\u70ed\u529b\u5b66\u7684\u6807\u51c6\u8bba\u8bc1\u603b\u662f\u7528\u5230\u5927\u6570\u6216\u9ad8\u7ef4<\/span>\uff08\u5373N\u2192\u221e\uff09<\/span>\u5047\u8bbe\u3002\u90a3\u4e48\uff0c\u7edf\u8ba1\u529b\u5b66\u53ef\u4ee5\u7528\u4e8e\u5c0f\u7cfb\u7edf\u6216\u4f4e\u7ef4\u7cfb\u7edf<\/strong><\/span>\uff08\u5373N\uff5e1\uff09<\/span>\u5417\uff1f<\/span><\/strong>\u7b14\u8005\u8bd5\u56fe\u7528\u53d7\u751f\u7269\u542f\u53d1\u7684\u7b2c\u4e09\u79cd\u666e\u9002\u529b\u5b66\u5bf9\u8fd9\u4e24\u4e2a\u95ee\u9898\u7ed9\u51fa\u80af\u5b9a\u56de\u7b54\uff0c\u5e0c\u671b\u80fd\u5f15\u8d77\u8bfb\u8005\u7684\u8fdb\u4e00\u6b65\u601d\u8003\u3002<\/span><\/p>\n


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\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u6587\u5b57\u65b9\u7a0b\u5df2\u5f88\u6e05\u695a\u5730\u8868\u660e\uff0c\u6f14\u5316\u8fc7\u7a0b\u662f\u4e00\u4e2a\u6982\u7387\u6027\u7684\u9012\u63a8\u5173\u7cfb\u3002\u4ece\u73b0\u4ee3\u8ba1\u7b97\u673a\u79d1\u5b66\u89d2\u5ea6\u770b\uff0c\u6f14\u5316\u662f\u4e00\u4e2a\u660e\u786e\u7684\u4e00\u822c\u7b97\u6cd5\uff1a\u5982\u4f55\u5f97\u5230\u4e0b\u4e00\u6b65\u7ed3\u679c\u3002\u4e0d\u96be\u770b\u51fa\uff0c\u6240\u6709\u7684\u7b97\u6cd5\u90fd\u5177\u6709\u8fd9\u6837\u7684\u7279\u5f81\uff0c\u5b83\u662f\u4e00\u4e2a\u666e\u9002\u7b97\u6cd5\u3002\u8fd9\u610f\u5473\u7740\u8fbe\u5c14\u6587\u529b\u5b66\u53ef\u4ee5\u5e94\u7528\u4e8e\u751f\u7269\u5b66\u4e4b\u5916\u7684\u9886\u57df\u3002<\/span><\/p>\n


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\u5bf9\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u666e\u9002\u7b97\u6cd5\u7406\u89e3\u5374\u4e0d\u80fd\u8ba9\u4eba\u5b8c\u5168\u6ee1\u610f\u3002\u9996\u5148\u8003\u8651\u4e00\u4e2a\u5b9e\u7528\u60c5\u5f62\u3002\u5047\u8bbe\u5df2\u77e5\u4e00\u4e2a\u6f14\u5316\u8fc7\u7a0b\uff0c\u4e5f\u5df2\u77e5\u5bf9\u5e94\u7684\u7b97\u6cd5\u3002\u7ed9\u5b9a\u521d\u59cb\u72b6\u6001\uff0c\u82e5\u60f3\u77e5\u9053\u957f\u65f6\u95f4\u4e4b\u540e\u7684\u53ef\u80fd\u72b6\u51b5\uff0c\u4ece\u7b97\u6cd5\u89d2\u5ea6\u53ea\u9700\u8981\u5728\u8ba1\u7b97\u673a\u4e0a\u8fd0\u884c\u5bf9\u5e94\u7684\u7a0b\u5e8f\u5373\u53ef\u3002\u5f53\u7136\uff0c\u53ef\u4ee5\u7528\u9002\u5f53\u7684\u751f\u7269\u8fc7\u7a0b\uff0c\u751a\u81f3\u7269\u7406\u8fc7\u7a0b\u6765\u5b9e\u73b0\u3002\u7531\u4e8e\u6211\u4eec\u7b97\u6cd5\u7684\u968f\u673a\u6027\uff0c\u9700\u8981\u8fdb\u884c\u591a\u6b21\u91cd\u590d\u6765\u53d1\u73b0\u5404\u79cd\u53ef\u80fd\u3002\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\uff0c\u5373\u4f7f\u8868\u9762\u4e0a\u7b80\u5355\u7684\u8ba1\u7b97\uff0c\u5176\u4ee3\u4ef7\u4e5f\u53ef\u80fd\u6781\u5176\u6602\u8d35\uff0c\u6216\u8005\u82b1\u8d39\u5927\u91cf\u65f6\u95f4\uff0c\u4ee5\u81f4\u6ca1\u6709\u5b9e\u7528\u6027\u3002\u9700\u8981\u5bfb\u6c42\u522b\u7684\u9014\u5f84\u3002\u4ece\u4eba\u7684\u672c\u6027\u6765\u8bf4\uff0c\u5373\u4f7f\u4e00\u4e2a\u7b97\u6cd5\u53ef\u4ee5\u7528\u8ba1\u7b97\u673a\u5f88\u597d\u5730\u5b9e\u73b0\uff0c\u4eba\u4eec\u4e5f\u5e76\u4e0d\u4e00\u5b9a\u6ee1\u610f\u8fd9\u6837\u201c\u8f93\u5165\u2014\u8f93\u51fa\u201d\u7684\u9ed1\u7bb1\u8fc7\u7a0b\uff0c\u66f4\u5e0c\u671b\u5bf9\u5176\u6709\u6574\u4f53\u7684\u4e86\u89e3\u3002\u4f8b\u5982\uff0c\u6f14\u5316\u8fc7\u7a0b\u4e2d\u7684\u201c\u9002\u5e94\u5ea6\u201d\u548c\u76f8\u5173\u7684\u201c\u8d8b\u5411\u5ea6\u201d\u8be5\u5982\u4f55\u5e94\u7528\u7b49\u3002\u7eaf\u7cb9\u4ece\u7b97\u6cd5\u89d2\u5ea6\u5f88\u96be\u5bf9\u6b64\u505a\u51fa\u4e00\u822c\u5224\u65ad\u3002<\/span><\/p>\n


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\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u7ed3\u6784<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u5728\u8fc7\u53bb100\u591a\u5e74\u4e2d\uff0c\u4eba\u4eec\u505a\u4e86\u5927\u91cf\u63a2\u7d22\uff0c\u91cf\u5316\u7684\u52aa\u529b\u4e5f\u4ece\u6765\u6ca1\u6709\u505c\u6b62\u8fc7\u3002\u4eba\u4eec\u53d1\u73b0\u4e86\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u4e24\u4e2a\u91cd\u8981\u7279\u5f81\u3002\u4e00\u662f\u81ea\u7136\u9009\u62e9\u57fa\u672c\u5b9a\u7406<\/strong>\uff0c\u7531\u8d39\u5e0c\u5c14<\/span>\uff08R. A. Fisher\uff09<\/span>\u63d0\u51fa\u3002\u8be5\u5b9a\u7406\u5f3a\u8c03\u53d8\u5f02\u4e0e\u6f14\u5316\u901f\u7387\u7684\u5173\u7cfb\u3002\u53e6\u4e00\u4e2a\u79f0\u4e3a\u6f14\u5316\u7684\u9002\u5e94\u6027\u666f\u89c2<\/strong>\uff0c\u7531\u83b1\u7279<\/span>\uff08S. Wright\uff09<\/span>\u63d0\u51fa\uff0c\u7528\u7c7b\u4f3c\u7269\u7406\u4e2d\u52bf\u80fd\u7684\u6982\u5ff5\u5f88\u597d\u63cf\u8ff0\u4e86\u751f\u7269\u6f14\u5316\u7684\u201c\u9002\u5e94\u5ea6\u201d\u3002\u5728\u53d1\u80b2\u751f\u7269\u5b66\u4e2d\uff0c\u534e\u4e01\u987f<\/span>\uff08C. H. Waddington\uff09<\/span>\u63d0\u51fa\u4e86\u540c\u7b49\u7684\u666f\u89c2\u6982\u5ff5\u3002\u7531\u4e8e\u76f8\u5173\u6570\u5b66\u5de5\u5177\u4e0d\u8db3\u548c\u751f\u7269\u7406\u8bba\u53d1\u5c55\u6ede\u540e\uff0c\u76f4\u5230\u6700\u8fd1\u8fd9\u4e24\u4e2a\u91cd\u8981\u6982\u5ff5\u4ecd\u4e00\u76f4\u5904\u4e8e\u4e89\u8bba\u72b6\u6001\u300221\u4e16\u7eaa\u4ee5\u6765\uff0c\u751f\u7269\u8fc7\u7a0b\u7684\u5b9a\u91cf\u7814\u7a76\u548c\u76f8\u5173\u7684\u6570\u5b66\u548c\u8ba1\u7b97\u5de5\u5177\u6709\u4e86\u957f\u8db3\u8fdb\u5c55\uff0c\u4f7f\u5f97\u89e3\u51b3\u5173\u4e8e\u81ea\u7136\u9009\u62e9\u7684\u57fa\u672c\u5b9a\u7406\u548c\u9002\u5e94\u6027\u666f\u89c2\u7684\u4e89\u8bba\u6210\u4e3a\u53ef\u80fd\u3002\u6211\u4eec\u53d1\u73b0\uff0c\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u666e\u9002\u7b97\u6cd5\u8868\u8ff0\u786e\u5b9e\u53ef\u4ee5\u8f6c\u5316\u4e3a\u4e00\u4e2a\u6709\u7ed3\u6784\u7684\u6570\u5b66\u65b9\u7a0b\uff0c\u9996\u5148\u6ce8\u610f\u5230\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u6587\u5b57\u65b9\u7a0b\u53ef\u76f4\u63a5\u7528\u6570\u5b66\u4e2d\u7684\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u9648\u8ff0<\/strong>\uff1a<\/span><\/p>\n


<\/span><\/p>\n

dq\/dt=f(q) +\u03b6(q, t).<\/span><\/p>\n


<\/span><\/p>\n

\u8fd9\u91cc\uff0c\u6f14\u5316\u7531\u76f8\u7a7a\u95f4\u7684\u901f\u5ea6dq\/dt\u8868\u793a\uff0c\u786e\u5b9a\u7684\u201c\u9009\u62e9\u529b\u201d\u7531f(q)\u8868\u793a\uff0c\u968f\u673a\u7684\u201c\u53d8\u5f02\u529b\u201d\u7531\u03b6(q,t)\u3002\u53d8\u91cfq\u5b9a\u4e49\u4e00\u4e2aN\u7ef4\u76f8\u7a7a\u95f4\uff0c\u53ef\u4e58\u6027\u968f\u673a\u91cf\u03b6(q,t)\u9009\u53d6\u4e3a\u9ad8\u65af\u767d\u566a\u97f3\u3002\u8be5\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u63cf\u8ff0\u4e86\u7cfb\u7edf\u5728\u76f8\u7a7a\u95f4\u4e2d\u7684\u52a8\u529b\u5b66\u6f14\u5316\u8fc7\u7a0b\uff0c\u5b83\u53ef\u4ee5\u7b49\u4ef7\u4e8e\u4e0b\u5217\u7ed3\u6784\u660e\u786e\u7684\u5f62\u5f0f\uff1a<\/span><\/p>\n


<\/span><\/p>\n

[A(q) +T(q)] dq\/dt = grad\u03c8(q) + \u03be(q,t).<\/span><\/p>\n


<\/span><\/p>\n

\u8fd9\u91cc\u52bf\u51fd\u6570\u03c8(q)\u91cf\u5316\u4e86\u9002\u5e94\u6027\u666f\u89c2\uff1b\u975e\u8d1f\u5bf9\u79f0N\u00d7N\u77e9\u9635A(q)\u548c\u968f\u673a\u6da8\u843d\u03be(q,t)\u7684\u5173\u7cfb\u91cf\u5316\u548c\u63a8\u5e7f\u4e86\u8d39\u5e0c\u5c14\u7684\u81ea\u7136\u9009\u62e9\u57fa\u672c\u5b9a\u7406\uff0c\u5bf9\u5e94\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u6da8\u843d\u2014\u8017\u6563\u5173\u7cfb\u3002\u77e9\u9635A(q)\u523b\u753b\u4e86\u6f14\u5316\u8fc7\u7a0b\u7684\u9002\u5e94\u6027\u3002\u8fd9\u4e2a\u65b9\u7a0b\u73b0\u5df2\u5e94\u7528\u4e8e\u751f\u7269\u8fc7\u7a0b\u7684\u5404\u4e2a\u65b9\u9762\uff0c\u5982\u566c\u83cc\u4f53\u03bb\u4e2d\u7684\u57fa\u56e0\u5f00\u5173\u3001\u79cd\u7fa4\u9057\u4f20\u52a8\u529b\u5b66\u3001\u4ee3\u8c22\u52a8\u529b\u5b66\u3001\u764c\u75c7\u4ea7\u751f\u548c\u53d1\u5c55\u7684\u5185\u6e90\u6027\u7f51\u7edc\u52a8\u529b\u5b66\u7b49\u3002\u53ef\u4ee5\u770b\u5230\uff0c [3]\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u8fdb\u4e00\u6b65\u770b\u5230\uff0c\u8fd9\u4e2a\u65b9\u7a0b\u662f\u8017\u6563\u4e0d\u4fdd\u5b88\u7684[A(q)\u22600]\uff0c\u4e14\u6ca1\u6709\u7ec6\u81f4\u5e73\u8861[T(q)\u22600]\uff0c\u4f46\u5b8c\u5168\u76f8\u5bb9\u4e8e\u7269\u7406\u5b66\u4e2d\u4fdd\u5b88\u7684\u57fa\u672c\u8fd0\u52a8\u65b9\u7a0b\u3002\u5047\u82e5 A(q)=0\u548c \u03be(q,t) =0\uff0c\u7279\u4f8b\u65b9\u7a0bT(q) dq\/dt=grad \u03c8(q) \u4fbf\u662f\u4eba\u4eec\u719f\u77e5\u7684\u54c8\u5bc6\u987f\u65b9\u7a0b\u3002\u8fd9\u4e2a\u7279\u4f8b\u4e5f\u8868\u660e\u53cd\u5bf9\u79f0\u77e9\u9635T(q) \u4ee3\u8868\u7740\u6f14\u5316\u8fc7\u7a0b\u4e2d\u7684\u5b88\u6052\u529b\u5b66\u3002\u5982\u679c\u7814\u7a76\u7684\u4f53\u7cfb\u7684\u7a33\u6001\u552f\u4e00\u5b58\u5728\uff0c\u5bf9\u5e94\u7684\u76f8\u7a7a\u95f4\u5206\u5e03\u51fd\u6570\u5c31\u7531\u52bf\u51fd\u6570 \u03c8(q) \u4ee5\u73bb\u5c14\u5179\u66fc\u2014\u5409\u5e03\u65af\u5206\u5e03\u7ed9\u5b9a\uff0c\u5373\u6b63\u5219\u5206\u5e03\u51fd\u6570\u3002\u6709\u4e86\u6b63\u5219\u5206\u5e03\uff0c\u5c31\u6709\u4e86\u70ed\u529b\u5b66\uff0c\u4e5f\u5c31\u6709\u4e86\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u3002\u73b0\u5728\u53ef\u4ee5\u505a\u51fa\u5982\u4e0b\u7ed3\u8bba\uff1a\u4f5c\u4e3a\u7a33\u6001\u6781\u9650\uff0c\u70ed\u529b\u5b66\u662f\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u903b\u8f91\u5fc5\u7136\uff1b\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u6210\u4e3a\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u7406\u3002\u65e2\u7136\u8fbe\u5c14\u6587\u529b\u5b66\u5305\u542b\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u8fd9\u6837\u7684\u666e\u9002\u89c4\u5f8b\uff0c\u5b83\u4e5f\u53ef\u4ee5\u662f\u4e00\u4e2a\u666e\u9002\u529b\u5b66\uff0c\u80fd\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5404\u4e2a\u9886\u57df\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u7ec6\u5fc3\u7684\u8bfb\u8005\u4f1a\u4ea7\u751f\u79d1\u5b66\u7406\u8bba\u65b9\u9762\u7684\u4e24\u4e2a\u56f0\u60d1\u3002\u7b2c\u4e00\u4e2a\u56f0\u60d1\u662f\u8fbe\u5c14\u6587\u529b\u5b66\u201c\u592a\u597d\u201d\u4e86\uff0c\u592a\u666e\u9002\u3002\u9664\u53bb\u5e26\u6709\u660e\u663e\u7279\u8bbe\u6027\u5047\u5b9a\u7684\u6f14\u5316\u7406\u8bba\uff0c\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u7b14\u8005\u8fd8\u4e0d\u80fd\u60f3\u8c61\u3001\u4e5f\u6ca1\u6709\u522b\u4eba\u53d1\u73b0\u4e00\u4e2a\u66ff\u4ee3\u7406\u8bba\uff0c\u5b83\u4f3c\u4e4e\u662f\u552f\u4e00\u7684\u666e\u9002\u7406\u8bba\u3002\u5f53\u7136\uff0c\u8bfb\u8005\u53ef\u4ee5\u8d23\u5907\u7b14\u8005\u7f3a\u5c11\u60f3\u8c61\u529b\u548c\u521b\u9020\u529b\u3002\u5148\u6682\u65f6\u63a5\u53d7\u76ee\u524d\u7684\u60c5\u5f62\uff0c\u8fbe\u5c14\u6587\u529b\u5b66\u4f3c\u4e4e\u603b\u662f\u5bf9\u7684\uff0c\u9887\u5177\u6709\u4e00\u70b9\u50cf\u6ce2\u666e\u5c14\u6240\u8bf4\u7684\u540c\u8bed\u53cd\u590d\u7684\u5473\u9053\u3002\u4f46\u4ece\u7b14\u8005\u53ca\u540c\u4e8b\u7684\u7814\u7a76\u7ecf\u5386\u6765\u770b\uff0c\u8fbe\u5c14\u6587\u529b\u5b66\u80af\u5b9a\u4e0d\u662f\u4e00\u4e2a\u540c\u8bed\u53cd\u590d\u7406\u8bba\u3002\u7b14\u8005\u66f4\u503e\u5411\u8fbe\u5c14\u6587\u529b\u5b66\u53cd\u6620\u4e86\u5b87\u5b99\u7684\u4e00\u4e2a\u6839\u672c\u7279\u6027\u3002<\/span><\/p>\n


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\u7b2c\u4e8c\u4e2a\u56f0\u60d1\u662f\u8fbe\u5c14\u6587\u529b\u5b66\u4e0d\u662f\u4e00\u4e2a\u6f14\u5316\u8fc7\u7a0b\u7684\u5168\u90e8\u63cf\u8ff0\u3002\u786e\u5b9e\u662f\u8fd9\u6837\u3002\u4ece\u8ba1\u7b97\u673a\u79d1\u5b66\u89d2\u5ea6\u770b\uff0c\u53ea\u6709\u7b97\u6cd5\u662f\u4e0d\u591f\u7684\uff0c\u8fd8\u9700\u8981\u7528\u5177\u4f53\u7684\u6750\u6599\u5177\u4f53\u5730\u5b9e\u73b0\u7b97\u6cd5\uff0c\u5982\u7528\u673a\u68b0\u88c5\u7f6e\u3001\u771f\u7a7a\u7535\u5b50\u7ba1\u3001\u6676\u4f53\u7ba1\uff0c\u6216\u901a\u8fc7\u522b\u7684\u65b9\u5f0f\u5236\u9020\u8ba1\u7b97\u673a\u3002\u751f\u7269\u5b66\u4e2d\uff0c\u6f14\u5316\u529b\u5b66\u7684\u5b9e\u73b0\u9700\u8981\u4e24\u90e8\u5206\u77e5\u8bc6\u6216\u4e24\u79cd\u89c4\u5f8b\uff1a\u5176\u4e00\u5c31\u662f\u529b\u5b66\u7ed3\u6784\u2014\u2014\u666e\u9002\u7684\u8fbe\u5c14\u6587\u529b\u5b66\uff1b\u5176\u4e8c\u662f\u5173\u4e8e\u6bcf\u4e2a\u529b\u5b66\u56e0\u7d20\u5982\u4f55\u5b9e\u73b0\u7684\u77e5\u8bc6\u3002\u4f8b\u5982\uff0c\u4e0a\u8ff0\u6587\u5b57\u65b9\u7a0b\u544a\u8bc9\u6211\u4eec\u4e09\u4e2a\u8981\u7d20\u9700\u8981\u88ab\u786e\u5b9a\uff1a<\/span><\/p>\n

\uff081\uff09\u4ec0\u4e48\u6837\u7684\u6f14\u5316\u8fc7\u7a0b\uff0c\u6709\u6027\u7e41\u6b96\u3001\u65e0\u6027\u7e41\u6b96\uff0c\u6216\u5176\u4ed6\uff1f<\/span><\/p>\n

\uff082\uff09\u968f\u673a\u53d8\u5f02\u662f\u5982\u4f55\u4ea7\u751f\u7684\uff0c\u662f\u751f\u7269\u4f53\u81ea\u5df1\u7684\u5185\u6e90\u56e0\u7d20\u8fd8\u662f\u73af\u5883\u7684\u5916\u5728\u56e0\u7d20\uff1f<\/span><\/p>\n

\uff083\uff09\u9009\u62e9\u88ab\u4ec0\u4e48\u4e3b\u5bfc\uff0c\u751f\u7269\u4f53\u7684\u5185\u7980\u7ed3\u6784\uff0c\u73af\u5883\u7684\u7279\u5f81\uff0c\u6216\u5b83\u4eec\u7684\u67d0\u4e2a\u7ec4\u5408\uff1f<\/span><\/p>\n

<\/span><\/span>\u5b9a\u91cf\u4e0a\uff0c\u8fd9\u5c31\u662f\u8981\u786e\u5b9a\u6570\u5b66\u65b9\u7a0b\u4e2d\u7684\u6bcf\u4e2a\u91cf: \u6070\u5f53\u7684\u72b6\u6001\u53d8\u91cf\u548c\u76f8\u7a7a\u95f4\u7684\u9009\u53d6\uff1b\u52bf\u51fd\u6570\u03c8\uff0c\u9002\u5e94\u6027\u77e9\u9635A\u548c\u4fdd\u5b88\u578b\u77e9\u9635T\u8be5\u5982\u4f55\u6784\u9020\uff1b\u968f\u673a\u6da8\u843d\u53ef\u901a\u8fc7F\u5b9a\u7406\u5bf9\u5e94\u4e8e\u9002\u5e94\u6027\u77e9\u9635A\u7b49\u3002\u5386\u53f2\u4e0a\uff0c\u8fbe\u5c14\u6587\u5bf9\u6f14\u5316\u529b\u5b66\u6709\u7740\u6e05\u6670\u8ba4\u8bc6\u2014\u2014\u6f14\u5316\u662f\u9009\u62e9\u548c\u53d8\u5f02\u7684\u534f\u540c\u4f5c\u7528\uff0c\u53ea\u662f\u751f\u7269\u8fc7\u7a0b\u7684\u4e00\u90e8\u5206\u89c4\u5f8b\u3002\u4ed6\u8feb\u5207\u9700\u8981\u53e6\u4e00\u90e8\u5206\u89c4\u5f8b\u2014\u2014\u9057\u4f20\u89c4\u5f8b\uff0c\u4f46\u4ed6\u6ca1\u6709\u627e\u5230\u6b63\u786e\u7684\u9057\u4f20\u89c4\u5f8b\u3002\u73b0\u5728\u77e5\u9053\uff0c\u5b5f\u5fb7\u5c14<\/span>\uff08J. Mendel\uff09<\/span>\u3001\u6c83\u68ee<\/span>\uff08J. Watson\uff09<\/span>\u548c\u514b\u91cc\u514b<\/span>\uff08F. Crick\uff09<\/span>\u6240\u53d1\u73b0\u7684\u57fa\u56e0\/DNA\u7ed3\u6784\u6b63\u662f\u8fbe\u5c14\u6587\u9700\u8981\u7684\u3002<\/span><\/p>\n


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\u6709\u6574\u4f53\u89c2\u5ff5\u503e\u5411\u7684\u8bfb\u8005\u4e5f\u8bb8\u4f1a\u8bf4\uff0c\u8fd9\u5e76\u975e\u662f\u4e00\u4e2a\u6574\u4f53\u7406\u8bba\uff0c\u751f\u7269\u5b66\u89c4\u5f8b\u88ab\u5272\u88c2\u6210\u4e24\u90e8\u5206\uff0c\u52a8\u529b\u5b66\u89c4\u5f8b\u548c\u5982\u4f55\u5b9e\u73b0\u52a8\u529b\u5b66\u8fc7\u7a0b<\/strong>\u3002\u786e\u5b9e\uff0c\u751f\u7269\u5b66\u4e2d\u8fd8\u6ca1\u6709\u4e00\u4e2a\u89c4\u5f8b\u80fd\u628a\u751f\u7269\u4e2d\u6240\u6709\u7684\u73b0\u8c61\u7edf\u4e00\u8d77\u6765\u3002\u5c31\u7b14\u8005\u76ee\u524d\u5173\u4e8e\u751f\u7269\u5b66\u7684\u4e0d\u5b8c\u5168\u77e5\u8bc6\u800c\u8a00\uff0c\u8fd9\u53ef\u80fd\u53cd\u800c\u662f\u4e00\u4ef6\u597d\u4e8b\u3002\u628a\u751f\u7269\u5b66\u89c4\u5f8b\u5206\u4e3a\u4e24\u90e8\u5206\u6709\u4e24\u4e2a\u4f18\u70b9\uff1a\u7b2c\u4e00\uff0c\u8fd9\u4e2a\u5212\u5206\u6e05\u695a\u5730\u8868\u660e\u8fbe\u5c14\u6587\u529b\u5b66\u662f\u666e\u9002\u7684\u3002\u5386\u53f2\u4e0a\u66fe\u591a\u6b21\u53d1\u751f\u628a\u5b9e\u73b0\u8fbe\u5c14\u6587\u529b\u5b66\u4e2d\u51fa\u73b0\u7684\u95ee\u9898\u9519\u8bef\u5730\u5f52\u5230\u8fbe\u5c14\u6587\u5934\u4e0a\uff0c\u4ee5\u81f4\u8d28\u7591\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u6b63\u786e\u6027\u3002\u6b64\u5916\uff0c\u5982\u679c\u8003\u5bdf\u4e00\u4e2a\u5178\u578b\u7684\u6574\u4f53\u7406\u8bba\u2014\u2014\u81ea\u7ec4\u7ec7\u7406\u8bba\uff0c\u5f88\u5bb9\u6613\u53d1\u73b0\u8fbe\u5c14\u6587\u529b\u5b66\u5728\u81ea\u7ec4\u7ec7\u4e4b\u524d\u3001\u4e4b\u4e2d\u3001\u4e4b\u540e\u90fd\u8d77\u4f5c\u7528\u3002\u7b2c\u4e8c\uff0c\u627f\u8ba4\u77e5\u8bc6\u7684\u4e0d\u5b8c\u5168\uff0c\u5e76\u5bf9\u540e\u7ee7\u8005\u6709\u4fe1\u5fc3\u3002\u672a\u6765\u7684\u8fbe\u5c14\u6587\u3001\u534e\u83b1\u58eb\u3001\u7231\u56e0\u65af\u5766\u4f1a\u5728\u524d\u4eba\u7684\u57fa\u7840\u4e0a\u505a\u51fa\u66f4\u597d\u3001\u66f4\u6df1\u523b\u7684\u5de5\u4f5c\uff0c\u5c06\u8d70\u5f97\u66f4\u8fdc\u3002<\/span><\/p>\n


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\u8fbe\u5c14\u6587\u529b\u5b66\u5bf9\u63a8\u52a8\u7269\u7406\u5b66\u7ee7\u7eed\u53d1\u5c55\u4e5f\u662f\u5fc5\u9700\u7684\u3002\u524d\u6587\u5df2\u63d0\u5230\u5b83\u80fd\u7ed9\u51fa\u70ed\u529b\u5b66\u7684\u903b\u8f91\u4e00\u81f4\u7684\u63a8\u5bfc\u3002\u4f5c\u4e3a\u53ef\u80fd\u7684\u7b2c\u4e09\u4e2a\u666e\u9002\u529b\u5b66\uff0c\u5e0c\u671b\u5b83\u8fd8\u80fd\u5177\u6709\u5df2\u77e5\u4e24\u4e2a\u666e\u9002\u529b\u5b66\u7684\u4e24\u4e2a\u7279\u5f81\uff1a\u666e\u9002\u5e38\u6570\u548c\u7269\u7406\u6781\u9650\u3002\u4f17\u6240\u5468\u77e5\uff0c\u91cf\u5b50\u529b\u5b66\u4e2d\u7684\u666e\u9002\u5e38\u6570\u662f\u666e\u6717\u514b\u5e38\u6570\uff0c\u72ed\u4e49\u76f8\u5bf9\u8bba\u4e2d\u7684\u666e\u9002\u5e38\u6570\u662f\u771f\u7a7a\u4e2d\u7684\u5149\u901f\uff1b\u91cf\u5b50\u529b\u5b66\u4e2d\u7684\u7269\u7406\u6781\u9650\u662f\u6d4b\u4e0d\u51c6\u5173\u7cfb\uff0c\u72ed\u4e49\u76f8\u5bf9\u8bba\u4e2d\u7684\u7269\u7406\u6781\u9650\u8fd8\u662f\u771f\u7a7a\u4e2d\u7684\u5149\u901f\u3002\u4ece\u4e0e\u7edf\u8ba1\u529b\u5b66\u548c\u70ed\u529b\u5b66\u7684\u5173\u7cfb\u6765\u770b\uff0c\u663e\u7136\u8fbe\u5c14\u6587\u529b\u5b66\u7684\u666e\u9002\u5e38\u6570\u662f\u73bb\u5c14\u5179\u66fc\u5e38\u6570\uff1b\u5b83\u63d0\u4f9b\u7684\u7269\u7406\u6781\u9650\u662f\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u7406\u3002<\/span><\/p>\n


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\u672c\u6587\u6839\u636e\u795d\u8d3a\u674e\u653f\u9053\u5148\u751f90\u534e\u8bde\u7684\u6587\u7a3f\u6539\u7f16\uff0c\u539f\u6587\u6536\u5f55\u5728\u300a\u5fc3\u901a\u5929\u5b87\u2014\u674e\u653f\u9053\u6559\u6388\u4e5d\u5341\u534e\u8bde\u6587\u96c6\u300b\u3002\u672c\u6587\u89c2\u70b9\u66fe\u53d7\u5230\u300a\u81ea\u7136\u00b7\u7269\u7406\u5b66\u300b\uff08Nature Physics<\/em>\uff09\u8bc4\u8bba\uff0c\u76ee\u524d\u79d1\u5b66\u754c\u8fd8\u6ca1\u6709\u5b8c\u6210\u76f8\u5e94\u7684\u5b9e\u9a8c\u68c0\u9a8c\uff0c\u5c1a\u6ca1\u6709\u5c31\u6b64\u7406\u8bba\u8fbe\u6210\u6700\u7ec8\u5171\u8bc6\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n

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\u53c2\u8003\u6587\u732e\uff1a<\/strong><\/span><\/section>\n
1. Lee T D, Yang C N. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Physical Review, 1952, 87(3): 410.<\/span><\/section>\n
2. The Cambridge companion to the philosophy of biology. New York : Cambridge University Press, 2007.<\/span><\/section>\n
3. Ao P. Laws in Darwinian evolutionary theory. Physics of Life Reviews, 2005, 2(2): 117-156.<\/span><\/section>\n
4. Yuan R S, Zhu X M, Wang G W, et al. Cancer as robust intrinsic state shaped by evolution: a key issues review. Reports on Progress in Physics, 2017,80(4), 042701.<\/span><\/section>\n
5. Silbey R, Ao P, Beretta G P, et al. Discussion on “Foundations of the Second Law”. AIP Conference Proceedings. AIP, 2008,1033(1): 198-204.<\/span><\/section>\n
6. Ao P. Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics. Communications in theoretical physics, 2008, 49(5): 1073.<\/span><\/section>\n
7. Yuan R, Ao P. Beyond It\u00f4 versus Stratonovich. Journal of Statistical Mechanics: Theory and Experiment, 2012, 2012(07): P07010.<\/span><\/section>\n
8. Qian H, Ao P, Tu Y, et al. A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales. Chemical Physics Letters, 2016, 665:153-161.<\/span><\/section>\n


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\u6556\u5e73\uff0c<\/strong>\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\uff0c\u5165\u9009\u4e0a\u6d77\u9886\u519b\u4eba\u624d\uff0c\u66fe\u4efb\u56fd\u5bb6\u201c973\u8ba1\u5212\u201d\u9996\u5e2d\u79d1\u5b66\u5bb6\u3002<\/span><\/section>\n

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\u96c6\u667a\u4ff1\u4e50\u90e8<\/span>\u300c\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60<\/a>\u300d\u8bfb\u4e66<\/span>\u4f1a\u6b64\u524d\u9080\u8bf7\u5230\u6556\u5e73\u8001\u5e08\u505a\u5173\u4e8e\u6f14\u5316\u529b\u5b66\u7684\u4e3b\u9898\u5206\u4eab\u3002\u4ed6\u66fe\u548c\u81ea\u7531\u80fd\u539f\u7406\u63d0\u51fa\u8005 Karl Friston \u5408\u4f5c\u4ece\u4e8b\u81ea\u7531\u80fd\u539f\u7406\u76f8\u5173\u7814\u7a76\uff0c\u57282012\u5e74\u53d1\u8868\u8bba\u6587 Free energy, value, and attractors\u3002\u6556\u5e73\u8001\u5e08\u8ba4\u4e3a\uff0c\u201c\u81ea\u7531\u80fd\u539f\u7406\u201d\u6709\u4e24\u5927\u57fa\u7840\uff1a \u79d1\u5b66\u57fa\u7840\u662f\u8fbe\u5c14\u6587\u6f14\u5316\u52a8\u529b\u5b66\uff0c\u6570\u5b66\u57fa\u7840\u662f\u968f\u673a\u8fc7\u7a0b\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u626b\u7801\u89c2\u770b\u89c6\u9891\u56de\u653e\u3002<\/span>\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>\u81ea\u7531\u80fd\u539f\u7406\u7684\u6f14\u5316\u529b\u5b66\u57fa\u7840\uff5c\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60\u8bfb\u4e66\u4f1a<\/a><\/span><\/p>\n

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\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60\u8bfb\u4e66\u4f1a<\/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\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\u88ab\u8ba4\u4e3a\u6709\u53ef\u80fd\u6210\u4e3a\u667a\u80fd\u7684\u7b2c\u4e00\u6027\u539f\u7406\u7684\u91cd\u8981\u5019\u9009\u65b9\u6848\uff0c\u5e76\u6709\u671b\u6210\u4e3a\u65b0\u65f6\u4ee3\u590d\u6742\u7cfb\u7edf\u7684\u5927\u7edf\u4e00\u7406\u8bba\u3002<\/span>\u96c6\u667a\u4ff1\u4e50\u90e8<\/span>\u300c\u81ea\u7531\u80fd\u539f\u7406\u4e0e\u5f3a\u5316\u5b66\u4e60\u300d\u8bfb\u4e66\u4f1a<\/a>\u9080\u8bf7\u5230 Karl Friston\u3001\u6556\u5e73\u3001\u725f\u7267\u4e91\u3001\u5f20\u6b63\u6cc9\u3001\u5f20\u5fb7\u7965\u3001\u9648\u6e5b\u3001\u4f55\u771f\u3001\u7f57\u51e1\u660e\u7b49\u7814\u7a76\u8005\uff0c\u4ece\u81ea\u7531\u80fd\u539f\u7406\u7684\u57fa\u7840\u7406\u8bba\u5230\u5f3a\u5316\u5b66\u4e60\u4e16\u754c\u6a21\u578b\u7b49\u524d\u6cbf\u5e94\u7528\uff0c\u7cfb\u7edf\u4ecb\u7ecd\u4e86\u81ea\u7531\u80fd\u539f\u7406\u4e3b\u52a8\u63a8\u7406\u6846\u67b6\u3002<\/span>\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u53c2\u4e0e\uff0c<\/span>\u548c<\/span>\u6211\u4eec\u4e00\u8d77\u5f00\u542f\u81ea\u7531\u80fd\u4e4b\u65c5\uff0c\u63a2\u7d22\u667a\u80fd\u7684\u7b2c\u4e00\u6027\u539f\u7406\uff01<\/span><\/section>\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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<\/section>\n
\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
1. <\/strong>\u81ea\u7531\u80fd\u539f\u7406\uff1a\u751f\u547d\u3001\u610f\u8bc6\u4e0e\u667a\u80fd\u7684\u7edf\u4e00\u539f\u7406<\/a><\/strong><\/span><\/strong><\/section>\n
2. <\/strong>\u65f6\u95f4\u4e3a\u4f55\u4e0d\u540c\u4e8e\u5176\u4ed6\u7ef4\u5ea6?<\/a><\/strong><\/span><\/strong><\/strong><\/section>\n
3.<\/strong> \u4ece\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u5230\u7b2c\u56db\u5b9a\u5f8b\uff1a\u5173\u4e8e\u7269\u7406\u3001\u751f\u547d\u3001\u4fe1\u606f\u3001\u8ba4\u77e5\u7684\u5927\u7edf\u4e00\u7406\u8bba<\/a><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n
4.<\/strong> \u524d\u6cbf\u7efc\u8ff0\uff1a\u63cf\u8ff0\u751f\u7269\u7cfb\u7edf\u6d8c\u73b0\u884c\u4e3a\u7684\u666f\u89c2\u548c\u6d41\u7406\u8bba\u89c6\u89d2<\/a><\/strong><\/span><\/strong><\/span><\/section>\n
5. <\/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
6.<\/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
7. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


<\/p>\n


<\/p>\n

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

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

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