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\u5728Boltzmann\u65b9\u7a0b\u7684\u57fa\u7840\u65b9\u9762\uff0c\u0411\u043e\u0433\u043e\u043b\u044e\u0301\u0431\u043e\u0432\uff081946\u5e74\uff09\u4f5c\u51fa\u4e86\u91cd\u8981\u7684\u8d21\u732e\u3002\u4ed6\u628a\u4f53\u7cfb\u968f\u65f6\u95f4\u7684\u53d8\u5316\u5206\u6210\u4e09\u4e2a\u9636\u6bb5\u6216\u4e09\u4e2a\u6807\u5ea6\u3002\u5728\u529b\u5b66\u6807\u5ea6\u4e0a\uff0c\u5206\u5e03\u51fd\u6570\u968f\u65f6\u95f4\u6709\u6025\u907f\u6691\u7684\u53d8\u5316\uff0c\u7cfb\u7edf\u987b\u8981\u6709\u591a\u7c92\u5b50\u7684\u5206\u5e03\u51fd\u6570\u6765\u63cf\u8ff0\uff1b\u5728\u52a8\u529b\u5b66\u6807\u5ea6\u4e0a\uff0c\u7cfb\u7edf\u7684\u5206\u5e03\u51fd\u6570\u8fc5\u901f\u5730\u5f00\u59cb\u201c\u540c\u6b65\u201d\u5316\uff0c\u8fd9\u65f6\u591a\u7c92\u5b50\u5206\u5e03\u51fd\u6570\u53ef\u8868\u793a\u4e3a\u5355\u7c92\u5b50\u5206\u5e03\u51fd\u6570\u7684\u6cdb\u51fd\uff0c\u53ea\u6709\u5355\u7c92\u5b50\u5206\u5e03\u51fd\u6570\u5c31\u80fd\u63cf\u8ff0\u7cfb\u7edf\u7684\u884c\u4e3a\uff1b\u6700\u540e\u5728\u6d41\u4f53\u529b\u5b66\u6807\u5ea6\u4e0a\uff0c\u5219\u53ea\u9700\u8981\u5206\u5e03\u51fd\u6570\u7684\u82e5\u5e72\u4e2a\u77e9\u5c31\u53ef\u4ee5\u63cf\u8ff0\u7cfb\u7edf\u7684\u884c\u4e3a\uff0c\u8fd9\u4e9b\u77e9\u91cf\u4e0e\u5c40\u90e8\u5b88\u6052\u91cf\u6709\u5173\u3002\u73b0\u4eca\uff0c\u56e0Born\u548cGreen\u3001Kirkwood\u53caYvon\u7684\u5171\u540c\u8d21\u732e\uff0c\u53ca\u6240\u5f97\u65b9\u7a0b\u7684\u7ea7\u8054\u5f62\u5f0f\uff0c\u6cbf\u4e0a\u8ff0\u601d\u8def\u6240\u5f97\u7684\u65b9\u7a0b\u5c31\u88ab\u79f0\u4e3aBBGKY\u7ea7\u8054\uff08hierarchy\uff09\u3002\u5728BBGKY\u7ea7\u8054\u4e2d\u4e5f\u987b\u4f5c\u7c7b\u4f3c\u5206\u5b50\u6df7\u6c8c\u7684\u5047\u8bbe\u3002\u0417\u0443\u0431\u0430\u0440\u0435\u8fdb\u4e00\u6b65\uff081961~1965\uff09\u53d1\u6325\u4e86\u0411\u043e\u0433\u043e\u043b\u044e\u0301\u0431\u043e\u0432\u7684\u6807\u5ea6\u601d\u60f3\uff0c\u5728\u6d41\u4f53\u529b\u5b66\u6807\u5ea6\u4e0a\u63d0\u51fa\u4e86\u5efa\u7acb\u5728\u5c40\u90e8\u5b88\u6052\u5f8b\u57fa\u7840\u4e0a\u7684\u9002\u7528\u4e8e\u4efb\u610f\u7cfb\u7edf\u7684\u975e\u5e73\u8861\u7edf\u8ba1\u7b97\u7b26\u3002\u975e\u5e73\u8861\u6001\u7edf\u8ba1\u7b97\u7b26\u5728\u6d41\u4f53\u529b\u5b66\u9636\u6bb5\u7684\u7406\u8bba\u57fa\u7840\u4e0e\u9002\u7528\u6027\u548cGibbs\u5bc6\u5ea6\u7b97\u7b26\u5bf9\u5e73\u8861\u6001\u7684\u7406\u8bba\u57fa\u7840\u4e0e\u9002\u7528\u6027\u76f8\u540c\uff0c\u5b83\u5bf9\u9ad8\u5bc6\u5ea6\u4e0e\u5f3a\u4f5c\u7528\u7cfb\u7edf\u4e0e\u5177\u6709\u666e\u904d\u6027\u3002<\/p>\n\n\n\n

\u5173\u4e8e\u591a\u4f53\u7cfb\u7edf\u8d8b\u5411\u5e73\u8861\u7684\u8ba4\u771f\u8ba8\u8bba\u59cb\u4e8eVan Hove\uff081955\uff09\u3002\u4ed6\u628a\u7cfb\u7edf\u80fd\u591f\u8d8b\u4e8e\u5e73\u8861\u5f52\u7ed3\u4e8e\u7cfb\u7edf\u672c\u8eab\u7684\u6027\u8d28\uff0c\u5373\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\u8d8b\u5411\u65e0\u7a77\uff08$N\\to\\infty$\u3001$V\\to\\infty$\u3001$N\/V=constant$\uff09\uff0c\u4e14\u77e9\u9635\u5143\u5177\u6709\uff08\u5bf9\u4e2d\u95f4\u6001\u6c42\u548c\u5f15\u8d77\u7684\uff09\u5bf9\u89d2\u5947\u5f02\u6027\u3002\u5bf9\u8fd9\u6837\u7684\u7cfb\u7edf\u53ea\u8981\u4f5c\u521d\u6001\u4e0e\u7ec8\u6001\u7684\u7c97\u7c92\u5316\uff0c\u5c31\u80fd\u83b7\u5f97\u8d8b\u5411\u5e73\u8861\u7684\u7ed3\u679c\u3002\u8fd9\u65b9\u9762\u7684\u5de5\u4f5c\u56e0Prigogine\u5b66\u6d3e\u7684\u957f\u671f\u5de5\u4f5c\u4e0eZwanzig\uff081960\u30011964\uff09\u5f15\u5165\u7684\u6295\u5f71\u7b97\u7b26\u65b9\u6cd5\uff0c\u800c\u65e5\u8d8b\u5b8c\u5584\u3002\u6839\u636e\u8fd9\u4e9b\u7814\u7a76\uff0cPrigogine\u5b66\u6d3e\u63d0\u51fa\u4e86\u8017\u6563\u6761\u4ef6\uff0c\u6ee1\u8db3\u8017\u6563\u6761\u4ef6\u7684\u7cfb\u7edf\u80fd\u591f\u8d8b\u5411\u5e73\u8861\u3002<\/p>\n\n\n\n

60\u5e74\u4ee3\u672b\u671f\u4ee5\u6765\uff0c\u7531\u4e8e\u6fc0\u5149\u3001\u6d41\u4f53\u4e0d\u7a33\u5b9a\u6027\u3001\u50ac\u5316\u53cd\u5e94\u7b49\u7684\u7814\u7a76\u53caPrigogine\u5b66\u6d3e\u548cHaken\u5b66\u6d3e\u7684\u5021\u5bfc\u4e0e\u5de5\u4f5c\uff0c\u5bf9\u5b8f\u89c2\u7cfb\u7edf\u7684\u975e\u5e73\u8861\u76f8\u53d8\uff08\u6216\u7a81\u53d8\uff09\u5f00\u5c55\u4e86\u5168\u9762\u7684\u7814\u7a76\u3002\u975e\u5e73\u8861\u76f8\u53d8\u53d1\u751f\u4e8e\u5bf9\u5e73\u8861\u504f\u79bb\u7684\u975e\u7ebf\u6027\u533a\u57df\uff0c\u56e0\u6b64\u5c5e\u4e8e\u8fdc\u79bb\u5e73\u8861\u7684\u60c5\u51b5\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u53ef\u80fd\u4f1a\u901a\u8fc7\u81ea\u7ec4\u7ec7\u5f62\u6210\u65b0\u7684\u975e\u5e73\u8861\u7ed3\u6784\u3002\u56e0\u6b64\uff0c\u8fd9\u4e2a\u9886\u57df\u7684\u7814\u7a76\u5bf9\u751f\u547d\u7684\u672c\u8d28\u548c\u793e\u4f1a\u7684\u6f14\u5316\u4e5f\u5177\u6709\u91cd\u8981\u7684\u610f\u4e49\u3002\u975e\u5e73\u8861\u76f8\u53d8\u5728\u8bb8\u591a\u5730\u65b9\u7c7b\u4f3c\u4e8e\u5e73\u8861\u76f8\u53d8\u3002\u5728\u76f8\u53d8\u70b9\u7684\u90bb\u57df\uff0c\u7531\u4e8e\u65e7\u6a21\u5f0f\u5c06\u53d8\u6210\u4e0d\u7a33\u5b9a\u4e0e\u65b0\u6a21\u5f0f\u5c06\u8981\u4ea7\u751f\uff0c\u4e34\u754c\u6da8\u843d\u662f\u751f\u91cd\u8981\u7684\u3002\u8fd9\u662f\u53e6\u4e00\u7c7b\u5f88\u6709\u610f\u601d\u7684\u4e0d\u540c\u4e8e\u8fd1\u5e73\u8861\u533a\u8f93\u8fd0\u8fc7\u7a0b\u7684\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u95ee\u9898\u3002<\/p>\n\n\n\n

60\u5e74\u4ee3\u4ee5\u6765\uff0c\u968f\u7740\u591a\u4f53\u95ee\u9898\u4e2dGreen\u51fd\u6570\u65b9\u6cd5\u7684\u53d1\u5c55\uff0c\u540c\u65f6\u4e5f\u5f62\u6210\u4e86\u5904\u7406\u975e\u5e73\u8861\u7cfb\u7edf\u7684Green\u51fd\u6570\u65b9\u6cd5\u3002\u5176\u4e2d\u5177\u6709\u4ee3\u8868\u6027\u7684\u662fKadanoff–Baym\u7684\u65f6\u95f4\u5ef6\u62d3\u6cd5\u4e0eSchrringer–Keldysh–\u5468–\u82cf–\u90dd–\u4e8e\u7684\u95ed\u8defGreen\u51fd\u6570\u65b9\u6cd5\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4e0d\u4fbf\u4e8e\u8ba8\u8bba\u8d8b\u5411\u5e73\u8861\u8fd9\u6837\u7684\u6839\u672c\u95ee\u9898\uff0c\u4f46\u6709\u5229\u4e8e\u5728\u6240\u9700\u7684\u4efb\u610f\u8fd1\u4f3c\u7a0b\u5ea6\u5185\u8ba8\u8bba\u5404\u79cd\u5b9e\u9645\u95ee\u9898\u3002<\/p>\n\n\n\n

\u6574\u4e2a\u6545\u4e8b\u5230\u8fd9\u91cc\u4f3c\u4e4e\u5e94\u8be5\u7ed3\u675f\u4e86\uff0c\u79d1\u5b66\u7684\u53d1\u5c55\u5374\u8868\u660e\u60c5\u51b5\u8fdc\u4e0d\u662f\u90a3\u4e48\u7b80\u5355\u7684\u3002Fermi–Pasta–Ulam\u57281950\u5e74\u901a\u8fc7\u6570\u503c\u5b9e\u9a8c\u53d1\u73b0\u975e\u7ebf\u6027\u6676\u683c\u5e76\u4e0d\u4f1a\u8868\u73b0\u51fa\u8d8b\u5411\u5e73\u8861\u7684\u73b0\u8c61\u3002\u73b0\u5728\u4eba\u4eec\u8ba4\u4e3a\u8fd9\u662f\u7531\u4e8e\u5b58\u5728\u5b64\u5b50\u89e3\u7684\u7f18\u6545\u3002\u6570\u5b66\u5bb6\u4eec\u53d1\u73b0\u7684KAM\uff08Kolmogorov–Arnold–Moser\uff09\u5b9a\u7406\u4e5f\u8868\u660e\uff1a\u5bf9\u4e8e\u5f31\u7684\u975e\u7b80\u8c10\u4f5c\u7528\uff0c\u632f\u5b50\u7cfb\u7edf\u7684\u8fd0\u52a8\u4ecd\u76f8\u4f3c\u4e8e\u7b80\u8c10\u7cfb\u7edf\u3002Toda\u6676\u683c\u7684\u7814\u7a76\u8868\u660e\uff0c\u751a\u81f3\u5bf9\u67d0\u4e9b\u7279\u6b8a\u7c7b\u578b\u7684\u5f3a\u975e\u7ebf\u6027\u4f5c\u7528\uff0c\u6676\u683c\u7cfb\u7edf\u4e5f\u4e0d\u4f1a\u8d8b\u5411\u5e73\u8861\u3002\u4f46\u662f\u8fd9\u6837\u7684\u7cfb\u7edf\u5982\u7528\u5fae\u6270\u6765\u5904\u7406\uff0c\u663e\u7136\u5177\u6709\u5bf9\u89d2\u5947\u5f02\u6027\uff0c\u56e0\u800c\u7528van Hove–Prigogine\u7406\u8bba\u6765\u8ba8\u8bba\uff0c\u5b83\u4e00\u5b9a\u4f1a\u8d8b\u5411\u5e73\u8861\u3002\u5b64\u5b50\u89e3\u7684\u5b58\u5728\u4e0eKAM\u5b9a\u7406\u8868\u660e\uff0cvan Hove–Prigogine\u7406\u8bba\u53ea\u662f\u63d0\u4f9b\u4e86\u67d0\u79cd\u5f62\u5f0f\uff0c\u53ea\u5229\u7528\u8fd9\u79cd\u5f62\u5f0f\u4e0d\u4e00\u5b9a\u4f1a\u5f97\u5230\u6b63\u786e\u7684\u7ed3\u679c\u3002\u4e8e\u662f\u90e8\u9898\u53c8\u53d8\u5f97\u4e00\u56e2\u7cdf\u4e86\u3002<\/p>\n\n\n\n

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[latexpage] \u6ce8\uff1a\u672c\u6587\u4f5c\u8005\u4e0d\u662f\u6211\uff0c\u800c\u662f\u4e00\u672c\u4f5a\u540d\u8bb2\u4e49\u7684\u7b2c\u4e00\u8282\u3002\u6211\u672c\u4eba\u5bf9\u8fd9\u6bb5\u6587\u5b57\u7684comment\u662f\uff0c\u867d\u5e74\u4ee3\u6709\u70b9\u8fc7\u65f6\uff0c\u4f46\u662f\u975e\u5e38accurate\uff0c\u5728\u90a3\u4e2a\u5e74\u4ee3\u7684\u4e2d\u6587\u8d44\u6599\u4e2d\u662f\u7f55\u89c1\u7684\u3002\u6401\u73b0\u5728\u4e5f\u662f\u975e\u5e38\u9ad8\u8d28\u91cf\u7684historical review + perspectives\u3002\u5e0c\u671b\u6709\u4eba\u80fd\u5e2e\u6211\u627e\u51fa\uff0c\u5b83\u7684\u4f5c\u8005\u662f\u8c01\u3002 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Hove\uff081955\uff09\u3002\u4ed6\u628a\u7cfb\u7edf\u80fd\u591f\u8d8b\u4e8e\u5e73\u8861\u5f52\u7ed3\u4e8e\u7cfb\u7edf\u672c\u8eab\u7684\u6027\u8d28\uff0c\u5373\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\u8d8b\u5411\u65e0\u7a77\uff08$N\\to\\infty$\u3001$V\\to\\infty$\u3001$N\/V=constant$\uff09\uff0c\u4e14\u77e9\u9635\u5143\u5177\u6709\uff08\u5bf9\u4e2d\u95f4\u6001\u6c42\u548c\u5f15\u8d77\u7684\uff09\u5bf9\u89d2\u5947\u5f02\u6027\u3002\u5bf9\u8fd9\u6837\u7684\u7cfb\u7edf\u53ea\u8981\u4f5c\u521d\u6001\u4e0e\u7ec8\u6001\u7684\u7c97\u7c92\u5316\uff0c\u5c31\u80fd\u83b7\u5f97\u8d8b\u5411\u5e73\u8861\u7684\u7ed3\u679c\u3002\u8fd9\u65b9\u9762\u7684\u5de5\u4f5c\u56e0Prigogine\u5b66\u6d3e\u7684\u957f\u671f\u5de5\u4f5c\u4e0eZwanzig\uff081960\u30011964\uff09\u5f15\u5165\u7684\u6295\u5f71\u7b97\u7b26\u65b9\u6cd5\uff0c\u800c\u65e5\u8d8b\u5b8c\u5584\u3002\u6839\u636e\u8fd9\u4e9b\u7814\u7a76\uff0cPrigogine\u5b66\u6d3e\u63d0\u51fa\u4e86\u8017\u6563\u6761\u4ef6\uff0c\u6ee1\u8db3\u8017\u6563\u6761\u4ef6\u7684\u7cfb\u7edf\u80fd\u591f\u8d8b\u5411\u5e73\u8861\u3002 60\u5e74\u4ee3\u672b\u671f\u4ee5\u6765\uff0c\u7531\u4e8e\u6fc0\u5149\u3001\u6d41\u4f53\u4e0d\u7a33\u5b9a\u6027\u3001\u50ac\u5316\u53cd\u5e94\u7b49\u7684\u7814\u7a76\u53caPrigogine\u5b66\u6d3e\u548cHaken\u5b66\u6d3e\u7684\u5021\u5bfc\u4e0e\u5de5\u4f5c\uff0c\u5bf9\u5b8f\u89c2\u7cfb\u7edf\u7684\u975e\u5e73\u8861\u76f8\u53d8\uff08\u6216\u7a81\u53d8\uff09\u5f00\u5c55\u4e86\u5168\u9762\u7684\u7814\u7a76\u3002\u975e\u5e73\u8861\u76f8\u53d8\u53d1\u751f\u4e8e\u5bf9\u5e73\u8861\u504f\u79bb\u7684\u975e\u7ebf\u6027\u533a\u57df\uff0c\u56e0\u6b64\u5c5e\u4e8e\u8fdc\u79bb\u5e73\u8861\u7684\u60c5\u51b5\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u53ef\u80fd\u4f1a\u901a\u8fc7\u81ea\u7ec4\u7ec7\u5f62\u6210\u65b0\u7684\u975e\u5e73\u8861\u7ed3\u6784\u3002\u56e0\u6b64\uff0c\u8fd9\u4e2a\u9886\u57df\u7684\u7814\u7a76\u5bf9\u751f\u547d\u7684\u672c\u8d28\u548c\u793e\u4f1a\u7684\u6f14\u5316\u4e5f\u5177\u6709\u91cd\u8981\u7684\u610f\u4e49\u3002\u975e\u5e73\u8861\u76f8\u53d8\u5728\u8bb8\u591a\u5730\u65b9\u7c7b\u4f3c\u4e8e\u5e73\u8861\u76f8\u53d8\u3002\u5728\u76f8\u53d8\u70b9\u7684\u90bb\u57df\uff0c\u7531\u4e8e\u65e7\u6a21\u5f0f\u5c06\u53d8\u6210\u4e0d\u7a33\u5b9a\u4e0e\u65b0\u6a21\u5f0f\u5c06\u8981\u4ea7\u751f\uff0c\u4e34\u754c\u6da8\u843d\u662f\u751f\u91cd\u8981\u7684\u3002\u8fd9\u662f\u53e6\u4e00\u7c7b\u5f88\u6709\u610f\u601d\u7684\u4e0d\u540c\u4e8e\u8fd1\u5e73\u8861\u533a\u8f93\u8fd0\u8fc7\u7a0b\u7684\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u95ee\u9898\u3002 60\u5e74\u4ee3\u4ee5\u6765\uff0c\u968f\u7740\u591a\u4f53\u95ee\u9898\u4e2dGreen\u51fd\u6570\u65b9\u6cd5\u7684\u53d1\u5c55\uff0c\u540c\u65f6\u4e5f\u5f62\u6210\u4e86\u5904\u7406\u975e\u5e73\u8861\u7cfb\u7edf\u7684Green\u51fd\u6570\u65b9\u6cd5\u3002\u5176\u4e2d\u5177\u6709\u4ee3\u8868\u6027\u7684\u662fKadanoff–Baym\u7684\u65f6\u95f4\u5ef6\u62d3\u6cd5\u4e0eSchrringer–Keldysh–\u5468–\u82cf–\u90dd–\u4e8e\u7684\u95ed\u8defGreen\u51fd\u6570\u65b9\u6cd5\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4e0d\u4fbf\u4e8e\u8ba8\u8bba\u8d8b\u5411\u5e73\u8861\u8fd9\u6837\u7684\u6839\u672c\u95ee\u9898\uff0c\u4f46\u6709\u5229\u4e8e\u5728\u6240\u9700\u7684\u4efb\u610f\u8fd1\u4f3c\u7a0b\u5ea6\u5185\u8ba8\u8bba\u5404\u79cd\u5b9e\u9645\u95ee\u9898\u3002 \u6574\u4e2a\u6545\u4e8b\u5230\u8fd9\u91cc\u4f3c\u4e4e\u5e94\u8be5\u7ed3\u675f\u4e86\uff0c\u79d1\u5b66\u7684\u53d1\u5c55\u5374\u8868\u660e\u60c5\u51b5\u8fdc\u4e0d\u662f\u90a3\u4e48\u7b80\u5355\u7684\u3002Fermi–Pasta–Ulam\u57281950\u5e74\u901a\u8fc7\u6570\u503c\u5b9e\u9a8c\u53d1\u73b0\u975e\u7ebf\u6027\u6676\u683c\u5e76\u4e0d\u4f1a\u8868\u73b0\u51fa\u8d8b\u5411\u5e73\u8861\u7684\u73b0\u8c61\u3002\u73b0\u5728\u4eba\u4eec\u8ba4\u4e3a\u8fd9\u662f\u7531\u4e8e\u5b58\u5728\u5b64\u5b50\u89e3\u7684\u7f18\u6545\u3002\u6570\u5b66\u5bb6\u4eec\u53d1\u73b0\u7684KAM\uff08Kolmogorov–Arnold–Moser\uff09\u5b9a\u7406\u4e5f\u8868\u660e\uff1a\u5bf9\u4e8e\u5f31\u7684\u975e\u7b80\u8c10\u4f5c\u7528\uff0c\u632f\u5b50\u7cfb\u7edf\u7684\u8fd0\u52a8\u4ecd\u76f8\u4f3c\u4e8e\u7b80\u8c10\u7cfb\u7edf\u3002Toda\u6676\u683c\u7684\u7814\u7a76\u8868\u660e\uff0c\u751a\u81f3\u5bf9\u67d0\u4e9b\u7279\u6b8a\u7c7b\u578b\u7684\u5f3a\u975e\u7ebf\u6027\u4f5c\u7528\uff0c\u6676\u683c\u7cfb\u7edf\u4e5f\u4e0d\u4f1a\u8d8b\u5411\u5e73\u8861\u3002\u4f46\u662f\u8fd9\u6837\u7684\u7cfb\u7edf\u5982\u7528\u5fae\u6270\u6765\u5904\u7406\uff0c\u663e\u7136\u5177\u6709\u5bf9\u89d2\u5947\u5f02\u6027\uff0c\u56e0\u800c\u7528van 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\u201c\u5c71\u7a77\u6c34\u5c3d\u7591\u65e0\u8def\uff0c\u67f3\u6697\u82b1\u660e\u53c8\u4e00\u6751\u3002\u201d\u5728\u8fd9\u7591\u96be\u7684\u5173\u5934\uff0c60\u5e74\u4ee3~70\u5e74\u4ee3\u671f\u95f4\u53d1\u5c55\u8d77\u6765\u7684\u52a8\u529b\u5b66\u7cfb\u7edf\u7406\u8bba\u548c\u6df7\u6c8c\u7406\u8bba\u7ed9\u6211\u4eec\u63d0\u4f9b\u4e86\u65b0\u7684\u7ebf\u7d22\u3002\u5206\u6790\u4e0e\u6570\u503c\u5b9e\u9a8c\u8868\u660e\uff1a\u5373\u4f7f\u5bf9\u4e00\u4e2a\u5c11\u81ea\u7531\u5ea6\u7684Hamilton\u7cfb\u7edf\uff0c\u7531\u4e8e\u975e\u7ebf\u6027\u4f5c\u7528\uff0c\u5b83\u4e5f\u4f1a\u8868\u73b0\u51fa\u67d0\u79cd\u7a0b\u5ea6\u7684\u904d\u5386\u6027\uff0c\u751a\u81f3\u66f4\u5f3a\u7684\u6df7\u5408\u6027\u3002\u5b64\u5b50\u7cfb\u7edf\u7684\u975e\u7ebf\u6027\u4e0d\u540c\u4e8e\u6df7\u6c8c\u7cfb\u7edf\u7684\u975e\u7ebf\u6027\uff0c\u5b64\u5b50\u7cfb\u7edf\u662f\u5b8c\u5168\u53ef\u79ef\u7684\uff0c\u800c\u6df7\u6c8c\u7cfb\u7edf\u662f\u4e0d\u53ef\u79ef\u7684\u3002\u6df7\u6c8c\u7cfb\u7edf\u7684\u7279\u70b9\u662f\u76f8\u7a7a\u95f4\u8f68\u9053\u4e3a\u9ad8\u5ea6\u4e0d\u7a33\u5b9a\u7684\uff0c\u957f\u65f6\u95f4\u7684\u884c\u4e3a\u5177\u6709\u6df7\u6c8c\u6027\uff0c\u56e0\u800c\u4f5c\u7c97\u7c92\u63cf\u8ff0\u65f6\u5c31\u5177\u6709\u8d8b\u5411\u5e73\u8861\u7684\u6027\u8d28\u3002\u5b83\u7ed9\u6211\u4eec\u63d0\u4f9b\u7684\u6e05\u6670\u7684\u8d8b\u5411\u5e73\u8861\u7684\u56fe\u50cf\uff0c\u6b63\u662f\u4eba\u4eec\u957f\u671f\u4ee5\u6765\u6240\u9884\u8a00\u4e0e\u671f\u671b\u7684\u3002\u4f46\u662f\u81f4\u4eca\u8fd8\u6ca1\u6709\u4eba\u80fd\u591f\u6839\u636e\u8fd9\u79cd\u56fe\u50cf\u505a\u51fa\u666e\u9002\u7684\u8d8b\u5411\u5e73\u8861\u7684\u7406\u8bba\u6765\u3002 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\u2014\u2014\u81f3\u4eca\u770b\u6765\u4ecd\u628a\u8be5\u4e66\u51fa\u7248\u65f6\uff081988\u5e74\uff09\u5df2\u7ecf\u5b9a\u578b\u7684\u7406\u8bba\u8ba4\u8bc6\u603b\u7ed3\u5f97\u5f88\u597d\u3002\u8fd9\u4e9b\u6a21\u578b\u53ef\u79f0\u4e3a\u9ad8\u5206\u5b50\u6eb6\u6db2\u7684\u6d41\u53d8\u5b66\u6027\u8d28\u7684\u201c\u7ecf\u5178\u6a21\u578b\u201d\u3002\u5b83\u4eec\u90fd\u662f\u6d41\u4f53\u52a8\u529b\u5b66\uff08hydrodynamic\uff09\u6a21\u578b\uff0c\u5373\u660e\u660e\u6eb6\u8d28\u5206\u5b50\uff08\u5bf9\u4e8e\u9ad8\u5206\u5b50\u6eb6\u8d28\u5219\u6307\u4e00\u4e2a\u94fe\u6bb5\u5355\u5143\uff09\u4e0e\u6eb6\u5242\u5206\u5b50\u7684\u5c3a\u5bf8\u548c\u8d28\u91cf\u5dee\u522b\u4e0d\u5927\uff0c\u5374\u89c6\u540e\u8005\u4e3a\u8fde\u7eed\u4ecb\u8d28\uff0c\u89c6\u524d\u8005\u4e3a\u60ac\u6d6e\u5728\u540e\u8005\u5f53\u4e2d\u53d1\u751f\u5e03\u6717\u8fd0\u52a8\u7684\u80f6\u4f53\u7c92\u5b50\u3002\u4e25\u683c\u610f\u4e49\u4e0a\uff0c\u8fd9\u6837\u7684\u6a21\u578b\u6240\u5f97\u51fa\u7684\u7ed3\u8bba\u5e94\u8be5\u53ea\u5728\u89c2\u6d4b\u65f6\u95f4\u5c3a\u5ea6\u5f88\u5927\u7684\u65f6\u5019\u6210\u7acb\uff0c\u5373\u6db2\u4f53\u975e\u5e73\u8861\u7edf\u8ba1\u4e2d\u7684\u6240\u8c13\u6d41\u4f53\u52a8\u529b\u5b66\u6781\u9650\uff08hydrodynamic limit\uff09\uff0c\u8be6\u89c1The Theory of Simple Liquids\u4e00\u4e66\u3002\u4f8b\u5982\uff0c\u5f39\u6027\u54d1\u94c3\u3001Rouse--Zimm\u548cDoi--Edwards\u6a21\u578b\u90fd\u5c5e\u4e8e\u6b64\u7c7b\u3002\u8fd9\u7c7b\u6a21\u578b\u7684\u5176\u4e2d\u4e00\u4e2a\u5171\u540c\u70b9\u662f\u90fd\u501f\u52a9\u4e86\u80f6\u4f53\u60ac\u6d6e\u6db2\u7684\u504f\u5e94\u529b\u5f20\u91cf\u7406\u8bba\u65b9\u6cd5\u3002\u8be5\u65b9\u6cd5\u7531Kramers\u63d0\u51fa\uff0cKirkwood\u96c6\u5927\u6210\u3002\u6b64\u5373\u4e3a\u8bb8\u8001\u5e08\u539f\u6587\u6240\u8bf4\u7684\u201c\u8ffd\u6eaf\u523040\u5e74\u4ee3\u201d\u3002\u8fd9\u4e00\u7406\u8bba\u65b9\u6cd5\u7528\u5230\u4e86Smoluschowski\u65b9\u7a0b\uff0c\u5176\u4e2d\u542b\u6709\u6d41\u4f53\u52a8\u529b\u5b66\u7684Oseen\u5f20\u91cf\u3002 \u76f8\u6bd4\u800c\u8a00\uff0c\u805a\u5408\u7269\u52a8\u529b\u5b66\u7684\u7b2c\u4e00\u539f\u7406\u6027\u6a21\u578b\u53d1\u5c55\u8f83\u665a\u3002\u6240\u8c13\u7b2c\u4e00\u539f\u7406\u6027\uff0c\u5373\u4ece\u5fae\u89c2\u5355\u5143\uff08\u805a\u5408\u7269\u94fe\u6bb5\u5355\u5143\u6216\u6eb6\u5242\u5206\u5b50\uff09\u7684Hamiltonian\u51fa\u53d1\u5efa\u7acb\u76f8\u7a7a\u95f4\u7684Liouville\u65b9\u7a0b\uff1b\u8fd0\u7528Zwanzig--Mori\u6295\u5f71\u7b97\u7b26\u6cd5\u83b7\u5f97\u4e00\u822c\u76f8\u7a7a\u95f4\u53d8\u91cf\u7684\u5e7f\u4e49Langevin\u65b9\u7a0b\uff1b\u518d\u8fd0\u7528\u67d0\u79cd\u6a21\u5f0f\u8026\u5408\u7406\u8bba\uff08mode-coupling theory\uff09\u6765\u5f97\u5230\u8bb0\u5fc6\u51fd\u6570\u548c\u5305\u62ec\u7c98\u5ea6\u5728\u5185\u7684\u5b8f\u89c2\u8f93\u9001\u6027\u8d28\u3002Zwanzig--Mori\u6295\u5f71\u7b97\u7b26\u6cd5\u53ef\u89c1Theory of Simple Liquids\u4e00\u4e66\u3002\u6a21\u5f0f\u8026\u5408\u7406\u8bba\u7531Kawasaki\u4e8e70\u5e74\u4ee3\u63d0\u51fa\u3002\u6700\u521d\u662f\u7528\u4e8e\u52a8\u529b\u5b66\u4e34\u754c\u884c\u4e3a\u7684\uff0c\u540e\u6765\u5e94\u7528\u4e8e\u975e\u4e34\u754c\u72b6\u6001\u7684\u4f53\u7cfb\u7684\u52a8\u529b\u5b66\uff0c\u53ef\u89c1Keyes\u7684\u7efc\u8ff01\u3002\u7b2c\u4e00\u4e2a\u5c06\u8fd9\u4e2a\u7406\u8bba\u6846\u67b6\u5e94\u7528\u4e8e\u805a\u5408\u7269\u4f53\u7cfb\u7684\u662fK. Schweizer\u3002\u5177\u4f53\u5230\u5e94\u529b\u5f20\u91cf\u6216\u7c98\u5ea6\u7684\u7406\u8bba\u63a8\u5bfc\u95ee\u9898\uff0c\u5728\u975e\u5e73\u8861\u7edf\u8ba1\u529b\u5b66\u4e2d\uff0c\u76ee\u524d\u53ea\u6709\u9884\u6d4b\u7ebf\u6027\u8f93\u8fd0\u65b9\u7a0b\u7684\u7406\u8bba\u2014\u2014\u7ebf\u6027\u54cd\u5e94\u7406\u8bba\u2014\u2014\u662f\u6bd4\u8f83\u6210\u719f\u7684\u3002\u81f3\u4e8e\u975e\u7ebf\u6027\u7406\u8bba\u7684\u8ba8\u8bba\uff0c\u53ef\u89c1Evans & Morriss\u8457\u4f5c\u7684\u76f8\u5173\u7ae0\u8282\u3002","rel":"","context":"In "\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0"","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8145,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8145","url_meta":{"origin":8923,"position":2},"title":"\u9ad8\u5206\u5b50\u4e13\u4e1a\u7684\u540c\u5b66\u600e\u4e48\u5b66\u6d41\u53d8\u5b66","author":"Andrew","date":"2021\u5e743\u670825\u65e5","format":false,"excerpt":"\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u662f\u6d41\u53d8\u5b66\u7684\u57fa\u7840\u3002\u800c\u5fc5\u8981\u7684\u7ebf\u6027\u4ee3\u6570\u548c\u5411\u91cf\u51fd\u6570\u5fae\u79ef\u5206\u53c8\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66 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equation\uff09\u3002\u8fd9\u4e9b\u90fd\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u9488\u5bf9\u725b\u987f\u6d41\u4f53\u7684\u5e94\u7528\u3002\u7136\u800c\uff0c\u7531\u4e8e\u300a\u5316\u5de5\u539f\u7406\u300b\u7684\u7814\u7a76\u76ee\u6807\u4ec5\u4e3a\u89e3\u51b3\u4f20\u8d28\u4f20\u70ed\u95ee\u9898\uff0c\u52a0\u4e0a\u6570\u5b66\u57fa\u7840\u8bbe\u7f6e\u4e0a\u7684\u9650\u5236\uff0c\u300a\u5316\u5de5\u539f\u7406\u300b\u8bfe\u7a0b\u4e2d\u7684\u5e94\u7528\u4f8b\u9898\u4e00\u822c\u4ec5\u9650\u4e8e\u5c42\u6d41\uff08\u7ebf\u6027\u5316\u7684\u7eb3\u7ef4--\u65af\u6258\u514b\u65af\u65b9\u7a0b\uff09\u3001\u4e00\u7ef4\u3001\u5b9a\u6001\u6d41\u95ee\u9898\uff0c\u751a\u81f3\u53ef\u4ee5\u8d8a\u8fc7\u7eb3\u7ef4--\u65af\u6258\u514b\u65af\u65b9\u7a0b\u7684\u660e\u663e\u5f15\u5165\uff0c\u76f4\u63a5\u91c7\u7528\u5fae\u79ef\u5206\u601d\u60f3\u5217\u51fa\u5fae\u5206\u65b9\u7a0b\u89e3\u9898\uff1b\u5f80\u5f80\u53ea\u5173\u5fc3\u538b\u5dee\u548c\u603b\u6d41\u91cf\u7684\u5173\u7cfb\u95ee\u9898\uff08\u4f8b\u5982Hagen--Poisseuille\u65b9\u7a0b\uff09\uff0c\u907f\u514d\u7ec6\u5316\u5230\u6d41\u901f\u5206\u5e03\u573a\u7b49\u6d89\u53ca\u573a\u51fd\u6570\u5fae\u79ef\u5206\u5b9a\u7406\u7684\u6570\u5b66\u77e5\u8bc6\u7684\u9898\u76ee\uff0c\u4ee5\u4fdd\u6301\u5168\u4e66\u7bc7\u5e45\u5728\u5408\u7406\u7684\u8303\u56f4\u5185\u3002 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\u03c3-\u4ee3\u6570\u2014\u2014\u800c\u4e14\u5bf9\u4efb\u4e00\u5c40\u57df$\\omega_t\\subset\\Lambda_t,\\omega_t\\in\\mathcal{B}$\uff0c\u6982\u7387\u90fd\u5b88\u6052\u3002\u8fd9\u4ef6\u4e8b\uff0c\u5728\u4f20\u7edf\u6559\u79d1\u4e66\u5f53\u4e2d\u662f\u7528\u7cfb\u7efc\u7684\u6982\u5ff5\uff0c\u7136\u540e\u8bf4\u201c\u7cfb\u7efc\u7684\u7cfb\u7edf\u6570\u91cf\u4e0d\u53d8\u201d\u6765\u8ba8\u8bba\u7684\u3002\u4ee5\u4e0b\u6211\u4eec\u4ece\u6982\u7387\u8bba\u7684\u89d2\u5ea6\u5efa\u7acb\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u7840\u3002 \u8003\u8651\u4e00\u4e2a\u7531$N$\u4e2a\u7c92\u5b50\u7ec4\u6210\u7684\u7cfb\u7edf\uff0c\u5728\u7edf\u8ba1\u529b\u5b66\u4e2d\uff0c\u8003\u8651\u7c92\u5b50\u6570$N$\u6052\u5b9a\u7684\u60c5\u51b5\u5df2\u7ecf\u8db3\u591f\u4e00\u822c\u3002\u5bf9\u4e8e\u7c92\u5b50\u6570\u53d8\u5316\u7684\u5f00\u653e\u7cfb\u7edf\uff0c\u7406\u8bba\u65b9\u6cd5\u4e0a\u603b\u662f\u901a\u8fc7\u6269\u5927\u7cfb\u7edf\u7684\u5212\u4efd\uff0c\u76f4\u81f3\u65b0\u7684\u7cfb\u7edf\u662f\u5c01\u95ed\u7684\uff08\u7c92\u5b50\u6570\u6052\u5b9a\uff09\uff0c\u7136\u540e\u57fa\u4e8e\u8fd9\u4e2a\u5927\u7cfb\u7edf\u7684\u6027\u8d28\u8ba8\u8bba\u5f53\u521d\u7684\u5c0f\u7cfb\u7edf\u4f5c\u4e3a\u5b50\u7cfb\u7edf\u7684\u6027\u8d28\u3002 \u5728\u7ecf\u5178\u529b\u5b66\u5047\u5b9a\u4e0b\uff0c\u7cfb\u7edf\u7684\u72b6\u6001\u603b\u662f\u53ef\u4ee5\u7531\u6240\u6709\u7c92\u5b50\u7684\u4f4d\u7f6e\u548c\u52a8\u91cf\u6240\u786e\u5b9a\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u7cfb\u7edf\u7684\u72b6\u6001\u603b\u662f\u5bf9\u5e94\u7740$6N$\u7ef4\u5b9e\u6570\u7a7a\u95f4$\\mathbb{R}^{6N}$\u4e2d\u7684\u4e00\u4e2a\u70b9$\\bm\\Gamma\\equiv\\left(\\mathbf{r}^N,\\mathbf{p}^N\\right)$\uff0c\u5176\u4e2d\u6211\u4eec\u7b80\u8bb0$\\mathbf{r}^N\\equiv\\left(\\mathbf{r}_1,\\cdots,\\mathbf{r}_N\\right)$\u548c$\\mathbf{p}^N\\equiv\\left(\\mathbf{p}_1,\\cdots,\\mathbf{p}_N\\right)$\u3002 \u7531\u4e8e\u6211\u4eec\u65e0\u6cd5\u786e\u5b9a\u7cfb\u7edf\u5728\u4efb\u4f55\u65f6\u523b\u7684\u5fae\u89c2\u72b6\u6001\uff0c\u56e0\u6b64\u6211\u4eec\u6bcf\u4e00\u65f6\u523b\uff0c\u90fd\u4e3a\u7cfb\u7edf\u53ef\u53d6\u7684\u6bcf\u4e00\u4e2a\u53ef\u80fd\u72b6\u6001\u8d4b\u4ee5\u6982\u7387\u3002\u5177\u4f53\u5730\uff0c\u8bbe$\\left(\\mathbb{R}^{6N},\\mathcal{B}\\right)$\u662f\u4e00\u4e2aBorel\u53ef\u6d4b\u7a7a\u95f4\uff0c$\\Lambda_t\\in\\mathcal{B}$\u8868\u793a\u7cfb\u7edf\u5728$t$\u65f6\u523b\u6240\u6709\u53ef\u53d6\u7684\u5fae\u89c2\u72b6\u6001\u7684\u96c6\u5408\uff0c$\\mu_t:\\mathcal{B}\\rightarrow\\left[0,1\\right]$\u662f\u5b9a\u4e49\u5728\u8fd9\u4e2a\u53ef\u6d4b\u7a7a\u95f4\u4e0a\u7684\u6982\u7387\u6d4b\u5ea6\uff0c$\\mu_t\\left[X\\right],X\\in\\mathcal{B}$\u8868\u793a$t$\u65f6\u523b\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001\u5728$X$\u5185\u7684\u6982\u7387\uff0c\u5b9e\u9645\u4e0a\\[\\mu_t\\left[X\\right]\\equiv\\int_Xf\\left(\\bm\\Gamma,t\\right)\\mathrm{d}\\bm\\Gamma\\]\u5176\u4e2d$f\\left(\\bm\\Gamma,t\\right)\\mathrm{d}\\bm\\Gamma$\u662f\u7cfb\u7edf\u5728$t$\u65f6\u523b\u5fae\u89c2\u72b6\u6001\u5904\u4e8e$\\bm\\Gamma\\sim\\bm\\Gamma+\\mathrm{d}\\Gamma$\u7684\u6982\u7387\u3002\u5141\u8bb8\u6982\u7387\u5bc6\u5ea6$f\\left(\\bm\\Gamma,t\\right)$\u5f97\u5230\u5b9a\u4e49\u6240\u9700\u8981\u7684$\\mu_t$\u5173\u4e8e$\\mathbb{R}^{6N}$\u7684\u52d2\u8d1d\u683c\u6d4b\u5ea6\u7684\u7edd\u5bf9\u8fde\u7eed\u6027\uff0c\u5b9e\u9645\u4e0a\u662f\u7531\u7ecf\u5178\u529b\u5b66\u672c\u8eab\u4fdd\u8bc1\u7684\uff0c\u89c1\u5173\u4e8e\u79bb\u6563\u6d4b\u5ea6\u6ca1\u6709\u5bc6\u5ea6\u7684\u95ee\u9898\u3002 \u5728\u7ecf\u5178\u529b\u5b66\u4e2d\uff0c\u7ed9\u5b9a\u67d0\u7cfb\u7edf\uff0c\u5b83\u7684\u8fd0\u52a8\u65b9\u7a0b\u603b\u662f\u628a\u4e00\u4e2a\u65f6\u523b$t$\u7684\u786e\u5b9a\u72b6\u6001$\\bm\\Gamma_t$\u6620\u5c04\u4e3a\u53e6\u4e00\u65f6\u523b$t+\\Delta t$\u7684\u552f\u4e00\u4e00\u4e2a\u786e\u5b9a\u72b6\u6001$\\bm\\Gamma_{t+\\Delta t}$\uff0c\u5373\u6211\u4eec\u53ef\u4ee5\u63d0\u53ca\u76f8\u5e94\u7684\u53cc\u5c04$\\chi_t:\\mathbb{R}^{6N}\\supset\\Lambda_t\\rightarrow\\mathbb{R}^{6N}$\u3002 \u82e5$\\Lambda_t\\in\\mathcal{B},\\omega_t\\in\\mathcal{B},\\omega_t\\subset\\Lambda_t,\\omega_{t+\\Delta t}=\\chi_t\\left(\\omega_t\\right)$\uff0c\u5219\u9996\u5148\u770b\u5230\u56e0\u4e3a$\\chi_t$\u5fc5\u662f\u8fde\u7eed\u7684\uff08\u7ecf\u5178\u529b\u5b66\u8fd0\u52a8\uff09\uff0c\u6545$\\chi_t$\u603b\u628a\u5f00\u96c6\u6620\u5c04\u4e3a\u5f00\u96c6\uff0c\u5373$\\omega_{t+\\Delta t}\\in\\mathcal{B}$\uff0c\u6545$\\chi_t$\u662f\u53ef\u6d4b\u6620\u5c04\u3002\u5176\u6b21\uff0c\u6211\u4eec\u770b\u5230\uff1a\\[\\mu_{t+\\Delta t}\\left(\\omega_{t+\\Delta t}\\right)=\\chi_t_*\\mu_t\\left(\\omega_t\\right)=\\mu_t\\left(\\chi_t^{-1}\\left(\\omega_{t+\\Delta t}\\right)\\right)=\\mu_t\\left(\\omega_t\\right)\\]\u5176\u4e2d\u8bb0\u53f7$f_*\\mu$\u8868\u793a\u6d4b\u5ea6$\\mu_t$\u7684\u7531\u53ef\u6d4b\u6620\u5c04$f$\u5f15\u51fa\u7684\u524d\u63a8\u6d4b\u5ea6\uff08pushforward measrue\uff09\uff0c\u4e0a\u9762\u7b2c\u4e8c\u4e2a\u7b49\u5f0f\u7528\u5230\u4e86\u524d\u63a8\u6d4b\u5ea6\u7684\u5b9a\u4e49\uff0c\u7b2c\u4e09\u4e2a\u7b49\u5f0f\u7528\u5230\u4e86$\\chi_t$\u7684\u53cc\u5c04\u6027\u3002\u4ee5\u4e0a\u63a8\u7406\u5bf9\u4efb\u610f$t,\\Delta t\\in\\mathbb{R}$\u4ee5\u53ca\u4efb\u610f$\\omega_t$\u5747\u6210\u7acb\u3002\u56e0\u6b64\u6211\u4eec\u8bc1\u660e\u4e86\uff0c$\\mathbb{R}^{6N}$\u7a7a\u95f4\u4efb\u4e00\uff08\u53ef\u6d4b\uff09\u5c40\u57df\u4e0a\u7684\u6982\u7387\u662f\u6cbf\u533a\u57df\u968f\u6309\u7167\u5b9e\u9645\u7cfb\u7edf\u8fd0\u52a8\u7684\u8fd0\u52a8\u7684\u5b88\u6052\u91cf\u3002\u56e0\u6b64\u6709\\[\\frac{\\mathrm{d}}{\\mathrm{d}t}\\mu_t\\left[\\omega_t\\right]\\equiv 0\\] \u540e\u7eed\u7531\u96f7\u8bfa\u4f20\u8f93\u5b9a\u7406\u5373\u53ef\u5f97\u5230\u5173\u4e8e\u6982\u7387\u5bc6\u5ea6\u51fd\u6570$f\\left(\\bm\\Gamma,t\\right)$\u7684\u5218\u7ef4\u5c14\u65b9\u7a0b\u3002","rel":"","context":"In "\u6211\u7684\u7814\u7a76\u7b14\u8bb0"","block_context":{"text":"\u6211\u7684\u7814\u7a76\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/rheo"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8206,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8206","url_meta":{"origin":8923,"position":4},"title":"\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u5386\u53f2\uff08\u4e00\uff09","author":"Andrew","date":"2021\u5e748\u670816\u65e5","format":false,"excerpt":"\u524d\u6bb5\u65f6\u95f4\u505a\u8fc7\u4e00\u4e9b\u5173\u4e8e\u7c98\u5f39\u6027\uff08viscoelasticity\uff09\u7684\u7814\u7a76\u5386\u53f2\u7684\u8d44\u6599\u8c03\u67e5\uff0c\u5c31\u5728\u6b64\u4f5c\u4e00\u4e9b\u4e0d\u5b8c\u6574\u7684\u603b\u7ed3\u3002 \u5b9e\u9645\u4e0aMaria Grazia Ianniello\u4f5c\u4e86\u5f88\u597d\u7684\u603b\u7ed3\u5de5\u4f5c\u200b(Ianniello 1993)\u200b\u200b*\u200b\uff0c\u6211\u5199\u7684\u5185\u5bb9\u5927\u90e8\u5206\u90fd\u662f\u76f4\u63a5\u6765\u81ea\u8fd9\u91cc\u3002\u5176\u5b9e\u6211\u4e5f\u72ec\u7acb\u5730\u8bc4\u4f30\u8fc7\u5979\u7684\u8bba\u6587\u3002\u6211\u81ea\u5df1\u770b\u8fc7\u4e00\u90e8\u5206\u7684\u5386\u53f2\u6587\u732e\u7684\u539f\u6587\uff08\u89c1\u6b64\u6587\uff09\uff0c\u518d\u53bb\u770bIanniello\u5bf9\u8fd9\u4e9b\u539f\u6587\u7684\u89e3\u8bfb\uff0c\u89c9\u5f97\u5979\u5173\u6ce8\u7ec6\u8282\u8ddf\u6211\u4e00\u6837\u591a\uff0c\u751a\u81f3\u770b\u5f97\u548c\u60f3\u5f97\u6bd4\u6211\u66f4\u4ed4\u7ec6\u3002\u79d1\u5b66\u54f2\u5b66\u5c42\u9762\u4e0a\u7684\u5173\u7167\u89d2\u5ea6\u4e5f\u548c\u6211\u5f88\u63a5\u8fd1\uff0c\u56e0\u6b64\u6211\u5f88\u4fe1\u8d56\u8fd9\u4e2a\u5de5\u4f5c\u3002\u53e6\u5916\u8fd8\u6709\u4e00\u7bc7\u66f4\u65e9\u4e9b\u7684\u79d1\u5b66\u53f2\u8bba\u6587\u200b(D\u00f6rries 1991)\u200b\uff0c\u4ece\u5e7f\u4e49\u7684\u201c\u4f59\u6548\u201d\uff08Nachwirking\uff09\u4e0e\u201c\u8fdf\u6ede\u201d\uff08histeresis\uff09\u6982\u5ff5\u7684\u89d2\u5ea6\u56de\u987e\u4e8619\u4e16\u7eaa\u7684\u7269\u7406\u5b66\u53f2\uff0c\u4f46\u662f\u63cf\u8ff0\u4e0d\u5982Ianniello\u7684\u6587\u7ae0\u8be6\u7ec6\u3002\u9664\u4e86\u8fd9\u4e9b\u79d1\u5b66\u53f2\u7814\u7a76\u8005\u7684\u8bba\u6587\u5916\uff0c\u6211\u5728\u8fd9\u91cc\u63d0\u4e00\u4e9b\u6d41\u53d8\u5b66\u5bb6\u81ea\u5df1\u505a\u7684\u5386\u53f2\u603b\u7ed3\u3002\u200b(Tanner and Walters 1998)\u200b\u7684\u8fd9\u672c\u4e66\u662f\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u4e00\u4e2a\u5927\u7684\u5386\u53f2\u603b\u7ed3\uff0c\u662f\u4e00\u4e2a\u5f88\u4f1f\u5927\u7684\u5de5\u7a0b\uff0c\u4f46\u662f\u96be\u514d\u4e5f\u6d41\u4e8e\u6cdb\u6cdb\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u7c97\u7565\u7684\u63d0\u7eb2\u548c\u53c2\u8003\u6587\u732e\u6765\u53c2\u8003\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cHershel Markovitz\u505a\u8fc7\u7684\u5f88\u591a\u6d41\u53d8\u5b66\u53f2\u603b\u7ed3\u66f4\u52a0\u95ee\u9898\u5bfc\u5411\u56e0\u800c\u4e5f\u66f4\u5bcc\u6709\u6d1e\u89c1\u200b(Markovitz 1968, 1977, 1985)\u200b\u3002\u200b(Doraiswamy 2002)\u200b\u4e5f\u505a\u4e86\u4e00\u4e2a\u5f88\u5168\u9762\u7684\u5386\u53f2\u6eaf\u6e90\u8d44\u6599\u603b\u7ed3\u3002\u200b(Tanner 2002)\u200b\u603b\u7ed3\u4e86\u6d41\u53d8\u6d4b\u91cf\u5b66\u4e2d\u6b63\u5f26\u6d4b\u8bd5\u65b9\u6cd5\u7684\u5386\u53f2\u3002 \u5df2\u6545\u7684\u6d41\u53d8\u5b66\u5bb6\u90d1\u878d\u8001\u5e08\u5728\u79d1\u5b66\u7f51\u4e0a\u7684\u535a\u5ba2\u5199\u6ee1\u4e86\u810d\u7099\u4eba\u53e3\u7684\u6d41\u53d8\u5b66\u53f2\u8bdd\u3002 1. \u4eca\u5929\u77e5\u9053\u7684\u201c\u7c98\u5f39\u6027\u201d \u201c\u7c98\u5f39\u6027\u201d\uff08viscoelasticity\uff09\u662f\u6d41\u53d8\u5b66\u6216\u529b\u5b66\u65b9\u9762\u7684\u8bcd\u3002 Ferry\u5bf9\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u5b8f\u89c2\u552f\u8c61\u7406\u8bba\u6a21\u578b\u548c\u5b9e\u9a8c\u65b9\u6cd5\u8fdb\u884c\u4e86\u5b8c\u6574\u7684\u603b\u7ed3\u200b(Ferry 1980)\u200b\u3002\u800c\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u5c31\u662f\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u7814\u7a76\u5bf9\u8c61\uff0c\u5176\u73b0\u8c61\u5b66\u6a21\u578b\u548c\u5b9e\u9a8c\u65b9\u6cd5\u53ef\u89c1\u4e8e\u5404\u4e2a\u6d41\u53d8\u5b66\u6559\u6750\u3002\u503c\u63d0\u4e00\u63d0\u7684\u662f\u632f\u8361\u6d4b\u8bd5\u5728\u975e\u7ebf\u6027\u54cd\u5e94\u4e2d\u7684\u63cf\u8ff0\u6846\u67b6\u5728\u6d41\u53d8\u5b66\u4e2d\u7684\u5e94\u7528\u662f\u201c\u5927\u5e45\u632f\u8361\u526a\u5207\u201d\uff08large amplitude oscillatory shear\uff0cLAOS\uff09\u3002\u8fd9\u65b9\u9762\u6700\u8fd1\u7684\u5927\u578b\u7efc\u8ff0\u200b(Hyun et al. 2011)\u200b\u5df2\u7ecf\u5f88\u65e9\u4e86\uff0c\u5176\u4e4b\u540e\u503c\u5f97\u5173\u6ce8\u7684\u76f8\u5173\u7efc\u8ff0\u6709\u200b(Bird and Giacomin 2016)\u200b\u548c\u200b(Voigtmann 2014)\u200b\u3002 \u4e8b\u5b9e\u4e0a\u7c98\u5f39\u6027\u7684\u73b0\u8c61\u5728\u529b\u5b66\u4e4b\u5916\u6709\u66f4\u4e00\u822c\u7684\u672c\u8d28\uff0c\u5b83\u5b9e\u8d28\u4e0a\u662f\u4e00\u79cd\u677e\u5f1b\uff08\u5f1b\u8c6b\uff09\u73b0\u8c61\u200b\u2020\u200b\uff0c\u5728\u7535\u78c1\u5b66\u4e2d\u4e5f\u5f88\u666e\u904d\u3002\u56e0\u6b64Oppenheim\u7684\u7ecf\u5178\u6559\u79d1\u4e66\u200b(Oppenheim et al. 1997)\u200b\u4e2d\u7684\u5f88\u591a\u65b9\u6cd5\u8ddf\u7c98\u5f39\u6027\u73b0\u8c61\u5b66\u662f\u76f8\u901a\u7684\u3002\u4f8b\u5982\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u901a\u7528\u672c\u6784\u2014\u2014Boltzmann\u65b9\u7a0b\u5c31\u662f\u4e00\u4e2a\u7ebf\u6027\u65f6\u4e0d\u53d8\u7cfb\u7edf\u7684\u5377\u79ef\u5f0f\u3002\u5728\u540e\u9762\u7684\u5386\u53f2\u4ecb\u7ecd\u4e2d\u6211\u4eec\u5c06\u4f1a\u770b\u5230\uff0c\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u53f2\u8ddf\u7535\u78c1\u5b66\u548c\u7535\u4fe1\u6280\u672f\u7684\u53d1\u5c55\u662f\u5bc6\u5207\u76f8\u5173\u7684\u3002\u4e00\u9886\u57df\u7684\u6982\u5ff5\u6216\u65b9\u6cd5\u5ef6\u7528\u4e8e\u53e6\u4e00\u9886\u57df\u7684\u60c5\u51b5\u5f88\u5e38\u89c1\uff0c\u4e14\u8fd9\u79cd\u60c5\u51b5\u4e00\u76f4\u5ef6\u7eed\u5230\u4eca\u5929\u3002 \u81f3\u4e8e\u5b8f\u89c2\u7c98\u5f39\u6027\u6216\u5176\u4ed6\u5b8f\u89c2\u6027\u8d28\u7684\u5f1b\u8c6b\u73b0\u8c61\u7684\u5fae\u89c2\u672c\u8d28\uff0c\u5219\u662f\u975e\u5e73\u8861\u6001\u7edf\u8ba1\u529b\u5b66\u63d0\u4f9b\u7684\u3002\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u8bf4\u5b8f\u89c2\u6027\u8d28\u7684\u5f1b\u8c6b\u73b0\u8c61\u7684\u5fae\u89c2\u672c\u8d28\u5c31\u662f\u70ed\u8fd0\u52a8\u3002\u5177\u4f53\u5730\uff0c\u7ebf\u6027\u54cd\u5e94\u7406\u8bba\u662f\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7edf\u8ba1\u57fa\u7840\u3002\u8fd9\u65b9\u9762\u5185\u5bb9\u53ef\u4ee5\u53c2\u8003\u200b(Evans and Morriss 2008)\u200b\u548c\u200b(Kreuzer 1981)\u200b\u3002 \u4e0a\u8ff0\u5f15\u7528\u7684\u8d44\u6599\u4ee3\u8868\u4e86\u6211\u4eec\u4eca\u5929\u5bf9\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u3002\u5728\u56de\u987e\u7c98\u5f39\u6027\u7684\u7814\u7a76\u5386\u53f2\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5c31\u81ea\u7136\u4f1a\u5173\u6ce8\u5f53\u65f6\u7684\u4eba\u4ece\u5f53\u65f6\u7684\u6570\u5b66\u548c\u7269\u7406\u5b66\u57fa\u7840\u548c\u5b9e\u9a8c\u73b0\u8c61\u6240\u80fd\u5f62\u6210\u7684\u6700\u521d\u8ba4\u8bc6\u8ddf\u4eca\u5929\u8ba4\u8bc6\u7684\u5dee\u5f02\u548c\u5dee\u8ddd\u662f\u600e\u6837\u7684\uff1f\u4e4b\u540e\u662f\u5982\u4f55\u201c\u677e\u5f1b\u201d\u5230\u4eca\u5929\u7684\u8ba4\u8bc6\u7684\uff1f 2. \u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e0e\u70ed\u529b\u5b66 \u6211\u4eec\u4eca\u5929\u7684\u8ba4\u8bc6\u4f53\u7cfb\u4e2d\uff0c\u7c98\u5f39\u6027\u73b0\u8c61\u662f\u5bf9\u7ecf\u5178\u7684\u864e\u514b\u5f39\u6027\u548c\u725b\u987f\u7c98\u6027\u7684\u63a8\u5e7f\u3002\u4ece\u66f4\u5927\u7684\u89d2\u5ea6\u770b\uff0c\u7c98\u5f39\u6027\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e2d\u7684\u7279\u6b8a\u672c\u6784\u5173\u7cfb\u3002\u4eca\u5929\u5982\u679c\u6211\u4eec\u8981\u8bb2\u8ff0\u7c98\u5f39\u6027\uff0c\u6211\u4eec\u4f1a\u5e0c\u671b\u542c\u4f17\u5df2\u7ecf\u5bf9\u4e0a\u8ff0\u8fd9\u4e9b\u80cc\u666f\u6709\u6240\u4e86\u89e3\u200b\u2021\u200b\u3002 \u9996\u5148\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u3002\u6b27\u62c9\u628a\u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b\u63a8\u5e7f\u81f3\u8fde\u7eed\u4ecb\u8d28\uff0c\u5e76\u63a8\u5bfc\u4e86\u521a\u4f53\u548c\u7406\u60f3\u6d41\u4f53\u7684\u65b9\u7a0b\u200b(Truesdell 1960a, 1968)\u200b\u200b\u00a7\u200b\u3002\u8fd9\u5927\u6982\u662f\u5341\u516b\u4e16\u7eaa\u4e2d\u53f6\u7684\u4e8b\u60c5\u3002 \u5173\u4e8e\u80fd\u91cf\u5b88\u6052\uff0c\u4e5f\u8bb8\u4f2f\u52aa\u5229\u7684\u5de5\u4f5c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u79cd\u4ee3\u8868\uff0c\u4ee5\u4ed61738\u5e74\u53d1\u8868\u7684Hydrodynamica\u4e3a\u6807\u5fd7\u200b(Truesdell 1960a, 1968)\u200b\u3002\u4f2f\u52aa\u5229\u65b9\u7a0b\uff0c\u5c31\u662f\u673a\u68b0\u80fd\u4e0e\u91cd\u529b\u52bf\u80fd\u4e4b\u95f4\u7684\u80fd\u91cf\u5b88\u6052\u3002\u4ec5\u8003\u8651\u8fd9\u4e24\u79cd\u80fd\u91cf\u4e4b\u95f4\u7684\u5b88\u6052\u662f\u7ecf\u5178\u529b\u5b66\u53d1\u5c55\u8fc7\u7a0b\u4e2d\u7684\u4e00\u4e2a\u4e3b\u8981\u7684\u95ee\u9898\u5f62\u5f0f\u3002\u70ed\u529b\u5b66\u610f\u4e49\u4e0a\u7684\u80fd\u91cf\u5b88\u6052\uff08\u5373\u4f5c\u4e3a\u516c\u8bbe\u7684\u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\uff09\uff0c\u5219\u4e0e\u70ed\u7684\u672c\u8d28\u95ee\u9898\u548c\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u8ba4\u8bc6\u7b49\u4e00\u540c\u7ea0\u7f20\u523019\u4e16\u7eaa\u4e2d\u671f\u624d\u7b97\u786e\u7acb\u3002\u2026","rel":"","context":"In 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