{"id":51961,"date":"2024-08-05T21:07:15","date_gmt":"2024-08-05T13:07:15","guid":{"rendered":"https:\/\/swarma.org\/?p=51961"},"modified":"2024-08-05T21:07:15","modified_gmt":"2024-08-05T13:07:15","slug":"%e5%89%8d%e6%b2%bf%e8%bf%9b%e5%b1%95%ef%bc%9a%e7%ba%bf%e6%80%a7%e9%9a%8f%e6%9c%ba%e8%bf%ad%e4%bb%a3%e7%b3%bb%e7%bb%9f%e7%9a%84%e7%b2%be%e7%a1%ae%e5%9b%a0%e6%9e%9c%e6%b6%8c%e7%8e%b0%e7%90%86%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=51961","title":{"rendered":"\u524d\u6cbf\u8fdb\u5c55\uff1a\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u7cbe\u786e\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff5cEntropy \u56e0\u679c\u4e0e\u590d\u6742\u7cfb\u7edf\u7279\u520a"},"content":{"rendered":"
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2014\u5e74\u81f3\u4eca\uff0c\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u5bb6 Erik Hoel \u3001\u4f26\u6566\u5e1d\u56fd\u7406\u5de5\u5b66\u9662\u590d\u6742\u7cfb\u7edf\u4e2d\u5fc3\u7684 Fernado E. Rosas \u7b49\u4eba\u76f8\u7ee7\u63d0\u51fa\u5e76\u62d3\u5c55\u4e86\u57fa\u4e8e\u4fe1\u606f\u8bba\u7684\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u6846\u67b6\uff0c\u56e0\u679c\u6d8c\u73b0\u7684\u5b9a\u4e49\u4ee5\u53ca\u5ea6\u91cf\u7684\u65b9\u6cd5\u7ed9\u51fa\u4e86\u5b9a\u91cf\u7684\u63cf\u8ff0\uff0c\u4e3a\u73b0\u5b9e\u4e2d\u5173\u4e8e\u751f\u6001\u73af\u5883\u3001\u6c14\u5019\u3001\u57ce\u5e02\u3001\u5927\u8111\u3001\u7ec6\u80de\u3001\u5206\u5b50\u7b49\u590d\u6742\u7cfb\u7edf\u7684\u6f14\u5316\u89c4\u5f8b\u7814\u7a76\u65b9\u6cd5\u63d0\u4f9b\u4e86\u5168\u65b0\u7684\u8bc4\u5224\u6307\u6807\u548c\u601d\u8def\u65b9\u5411\uff0c\u8fd8\u6709\u671b\u4e3a\u56de\u7b54\u751f\u547d\u3001\u610f\u8bc6\u3001\u81ea\u7531\u610f\u5fd7\u7b49\u54f2\u5b66\u95ee\u9898\u63d0\u4f9b\u6d1e\u5bdf\u3002<\/span><\/strong><\/section>\n

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\u4e3a\u4e86\u7ee7\u7eed\u62d3\u5c55\u5e76\u5b8c\u5584\u56e0\u679c\u6d8c\u73b0\u7684\u76f8\u5173\u6846\u67b6\uff0c\u5e76\u4e3a\u89e3\u51b3\u771f\u5b9e\u590d\u6742\u7cfb\u7edf\u6f14\u5316\u95ee\u9898\u642d\u6865\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7cfb\u7edf\u79d1\u5b66\u5b66\u9662\u7855\u58eb\u7814\u7a76\u751f\u5218\u51ef\u5a01\u7b49\u4eba\u63d0\u51fa\u4e86\u4e00\u5957\u9488\u5bf9\u5df2\u77e5\u6a21\u578b\u56e0\u679c\u6548\u5e94\u7684\u7cbe\u786e\u5ea6\u91cf\u2014\u2014\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u4e0d\u4ec5\u4e3a\u4ee5\u5f80\u7684\u7814\u7a76\u63d0\u4f9b\u4e86\u7406\u8bba\u652f\u6491\uff0c\u8fd8\u5bf9\u672a\u6765\u7684\u9488\u5bf9\u5176\u4ed6\u7269\u7406\u6a21\u578b\u4ee5\u53ca\u771f\u5b9e\u590d\u6742\u7cfb\u7edf\u7684\u7814\u7a76\u94fa\u8def\u3002<\/span><\/strong>\u5728\u96c6\u667a\u4ff1\u4e50\u90e8\u300c\u56e0\u679c\u6d8c\u73b0\u300d\u8bfb\u4e66\u4f1a\u7b2c\u4e94\u5b63<\/a>\uff0c\u5218\u51ef\u5a01\u4ecb\u7ecd\u4e86\u53d1\u8868\u4e8eEntropy\u7684\u8fd9\u9879\u6700\u65b0\u7814\u7a76\uff0c\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u52a0\u5165\u8bfb\u4e66\u4f1a\u89c2\u770b\u89c6\u9891\u56de\u653e\u3002<\/span><\/strong><\/section>\n<\/section>\n
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\u56e0\u679c\u6d8c\u73b0\u7684\u91cf\u5316\u662f\u8fd1\u671f\u65b0\u5174\u8d77\u7684\u7814\u7a76\u65b9\u5411\uff0c\u4ee3\u8868\u7684\u662fErik Hoel\u63d0\u51fa\u4e86\u56e0\u679c\u6d8c\u73b0\u7684\u6700\u521d\u5b9a\u91cf\u7406\u8bba[1-3]\u3002\u56e0\u679c\u6548\u5e94\u901a\u8fc7\u6709\u6548\u4fe1\u606f<\/span>\uff08Effective Information\uff0c\u7b80\u79f0EI\uff09<\/span>\u6307\u6807\u6765\u91cf\u5316\uff0c\u82e5\u51fa\u73b0\u5b8f\u89c2\u6709\u6548\u4fe1\u606f\u5927\u4e8e\u5fae\u89c2\u6709\u6548\u4fe1\u606f\uff0c\u5219\u610f\u5473\u7740\u56e0\u679c\u6d8c\u73b0\u7684\u4ea7\u751f\u3002NIS\u4e0eNIS+\u7684\u76f8\u5173\u673a\u5668\u5b66\u4e60\u6846\u67b6\u5728\u6570\u503c\u89e3\u4e0a\u5b9e\u73b0\u4e86\u5bf9\u6700\u4f73\u7c97\u7c92\u5316\u7b56\u7565\u7684\u5bfb\u627e\u4e0eEI\u7684\u8ba1\u7b97[4,5]\u3002<\/span><\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/section>\n
An Exact Theory of Causal Emergence for Linear Stochastic  Iteration Systems<\/span><\/section>\n
\u8bba\u6587\u5730\u5740\uff1a<\/span><\/section>\n
https:\/\/doi.org\/10.3390\/e26080618<\/span><\/section>\n<\/blockquote>\n

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\u6211\u4eec\u8fd1\u671f\u5728 Entropy \u300c\u56e0\u679c\u4e0e\u590d\u6742\u7cfb\u7edf\u300d\u7279\u520a\u4e0a\u53d1\u8868\u7684\u6700\u65b0\u7814\u7a76\u2014\u2014\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u7cbe\u786e\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\uff0c\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u89e3\u91ca\u4e86\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u4ea7\u751f\u56e0\u679c\u6d8c\u73b0\u7684\u539f\u56e0\u548c\u673a\u7406<\/strong>\uff0c\u5e76\u6307\u660e\u4e86\u5728\u566a\u58f0\u662f\u6b63\u6001\u5206\u5e03\u7684\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u534f\u65b9\u5dee\u7684\u5927\u5c0f\u4ee5\u53ca\u52a8\u529b\u5b66\u53c2\u6570\u77e9\u9635\u7684\u7279\u5f81\u503c\uff0c\u5bf9\u7cfb\u7edf\u53ef\u5426\u4ea7\u751f\u56e0\u679c\u6d8c\u73b0\u6709\u91cd\u8981\u7684\u5f71\u54cd\uff1b\u968f\u540e\u5bf9\u4e8e\u4e0d\u540c\u7684\u53c2\u6570\u77e9\u9635\u4e0e\u968f\u673a\u566a\u58f0\uff0c\u53ef\u4ee5\u9488\u5bf9\u56e0\u679c\u6d8c\u73b0\u7684\u6700\u5927\u5316\uff0c\u7ed9\u51fa\u6700\u4f18\u7684\u7c97\u7c92\u5316\u6620\u5c04\u7684\u53c2\u6570\u77e9\u9635\u3002\u4e3a\u4e86\u9a8c\u8bc1\u76f8\u5173\u547d\u9898\uff0c\u8bba\u6587\u4e2d\u5c06\u5206\u6790\u7684\u6a21\u578b\u5e94\u7528\u4e8e\u4e09\u4e2a\u7b80\u5316\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u5c06\u7ed3\u679c\u4e0e\u6570\u503c\u6a21\u62df\u8fdb\u884c\u6bd4\u8f83\u3002<\/span><\/section>\n

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\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u53ef\u4ee5\u5206\u89e3\u4e3a\u786e\u5b9a\u6027\u0394J<\/span>1<\/sub>\u548c\u7b80\u5e76\u6027\u0394<\/span>J2<\/sub>\u4e24\u9879\uff0c\u786e\u5b9a\u6027<\/strong>\u63cf\u8ff0\u7cfb\u7edf\u524d\u4e00\u65f6\u523b\u72b6\u6001\u5df2\u77e5\u7684\u60c5\u51b5\u4e0b\uff0c\u540e\u4e00\u65f6\u523b\u7684\u968f\u673a\u6027\uff0c\u8d8a\u5c0f\u7684\u968f\u673a\u6027\u4ee3\u8868\u786e\u5b9a\u6027\u8d8a\u5f3a\uff0c\u8d8a\u5bb9\u6613\u5bf9\u7cfb\u7edf\u7684\u672a\u6765\u8d8b\u52bf\u8fdb\u884c\u9884\u6d4b\u3002\u7b80\u5e76\u6027<\/strong>\u63cf\u8ff0\u540e\u4e00\u65f6\u523b\u5df2\u77e5\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u524d\u4e00\u65f6\u523b\u7684\u53ef\u6eaf\u56e0\u6027\uff0c\u7b80\u5e76\u6027\u8d8a\u5f31\uff0c\u5bfc\u81f4\u7cfb\u7edf\u5f53\u524d\u72b6\u6001\u7684\u539f\u56e0\u5c31\u8d8a\u660e\u786e\u3002\u786e\u5b9a\u6027\u8d8a\u5f3a\uff0c\u7b80\u5e76\u6027\u8d8a\u5f31\uff0c\u6709\u6548\u4fe1\u606f\u5219\u4f1a\u8d8a\u5927\uff0c\u56e0\u679c\u6548\u5e94\u8d8a\u5f3a\u3002\u800c\u5fae\u89c2\u548c\u5b8f\u89c2\u786e\u5b9a\u6027\u548c\u7b80\u5e76\u6027\u7684\u53d8\u5316\u5206\u522b\u5f71\u54cd\u4e86\u56e0\u679c\u6d8c\u73b0\u7684\u5927\u5c0f\u3002<\/span><\/section>\n

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\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u5e94\u7528\u6848\u4f8b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5728\u77e5\u9053\u56e0\u679c\u6d8c\u73b0\u7684\u6700\u4f18\u89e3\u4e4b\u540e\uff0c\u6587\u7ae0\u4f7f\u7528\u63a8\u5bfc\u51fa\u7684\u5b9a\u7406\u6765\u5206\u6790\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u51e0\u79cd\u60c5\u51b5\uff0c\u5c1d\u8bd5\u5728\u5177\u6709\u5df2\u77e5\u52a8\u529b\u5b66\u7684\u7cfb\u7edf\u4e2d\u5bfb\u627e\u56e0\u679c\u6d8c\u73b0\u7684\u6700\u5927\u503c\u3002\u4e09\u4e2a\u6848\u4f8b\u662f\u5bf9\u56e0\u679c\u6d8c\u73b0\u7cbe\u786e\u7406\u8bba\u7684\u652f\u6491\uff0c\u4e5f\u662f\u4e3a\u672a\u6765\u53ef\u80fd\u89e3\u51b3\u6848\u4f8b\u63d0\u4f9b\u65b9\u5411\u3002<\/span><\/section>\n

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\u4e09\u7ef4\u7a7a\u95f4\u7684\u65cb\u8f6c\u6a21\u578b<\/span><\/strong><\/span><\/h4>\n

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\u901a\u8fc7\u5b9e\u9a8c\u7ed3\u679c\u53ef\u4ee5\u53d1\u73b0\uff0c\u5176\u5b9e\u56e0\u679c\u6d8c\u73b0\u7684\u4e3b\u8981\u539f\u56e0\u5c31\u662f\u5728\u7a7a\u95f4\u4e2d\uff0c\u7cfb\u7edf\u7684\u6f14\u5316\u867d\u7136\u5904\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u4f46\u662f\u53ea\u4f9d\u6258\u4e8e\u4e00\u6761\u4e00\u7ef4\u7684\u76f4\u7ebf\u6216\u8005\u4e00\u4e2a\u4e8c\u7ef4\u5e73\u9762\uff0c\u5c31\u53ef\u4ee5\u8fd1\u4f3c\u51fa\u7cfb\u7edf\u7684\u6f14\u5316\u89c4\u5f8b\u3002\u5982\u679c\u7c92\u5b50\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u56f4\u7ed5\u4e00\u6761\u76f4\u7ebf\u8fdb\u884c\u8fd0\u52a8\uff0c\u5e76\u4e14\u6536\u655b\u4e8e\u8be5\u76f4\u7ebf\uff0c\u90a3\u4e48\u76f4\u7ebf\u65b9\u5411\u7684\u6f14\u5316\u53ef\u4ee5\u89c6\u4e3a\u68af\u5ea6\u6d41\uff0c\u800c\u4e0e\u76f4\u7ebf\u5782\u76f4\u7684\u5e73\u9762\u4e0a\u7684\u6f14\u5316\u53ef\u4ee5\u89c6\u4e3a\u87ba\u7ebf\u7ba1\u6d41\uff0c\u7b80\u8a00\u4e4b\uff0c\u5c31\u662f\u76f4\u7ebf\u4e0a\u53ef\u4ee5\u66f4\u6e05\u6670\u7684\u89c2\u6d4b\u5230\u7cfb\u7edf\u7684\u6f14\u5316\u65b9\u5411\u3002\u56e0\u6b64\u4f1a\u5728\u538b\u7f29\u5230\u4e00\u7ef4\u65f6\u4ea7\u751f\u8f83\u5927\u7684\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n

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\u5982\u679c\u7cfb\u7edf\u662f\u6536\u655b\u5230\u4e00\u4e2a\u5e73\u9762\uff0c\u90a3\u4e48\u8be5\u5e73\u9762\u80fd\u53cd\u6620\u7cfb\u7edf\u7684\u6f14\u5316\u65b9\u5411\uff0c\u8fd9\u65f6\u538b\u7f29\u5230\u4e8c\u7ef4\uff0c\u4f1a\u4ea7\u751f\u6700\u5927\u7684\u56e0\u679c\u6d8c\u73b0\u3002\u7531\u4e8e\u65cb\u8f6c\u77e9\u9635\u4f1a\u51fa\u73b0\u590d\u6570\u7279\u5f81\u6839\uff0c\u6211\u4eec\u6839\u636e\u7279\u5f81\u6839\u7684\u6a21\u957f\u8ba1\u7b97\u56e0\u679c\u6d8c\u73b0\uff0c\u4e4b\u6240\u4ee5\u4e0d\u538b\u7f29\u5230\u4e00\u7ef4\uff0c\u662f\u56e0\u4e3a\u524d\u4e24\u4e2a\u7279\u5f81\u503c\u662f\u5171\u8f6d\u590d\u6570\uff0c\u6a21\u957f\u76f8\u7b49\uff0c\u538b\u7f29\u5230\u4e00\u7ef4\u4e0d\u4f1a\u589e\u5f3a\u56e0\u679c\u6d8c\u73b0\uff0c\u53cd\u800c\u4f1a\u4f7f\u8bef\u5dee\u53d8\u5f97\u66f4\u5927\u3002<\/span><\/section>\n

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\u65cb\u8f6c\u6a21\u578b\u4e3a\u56e0\u679c\u6d8c\u73b0\u7684\u610f\u4e49\u63d0\u4f9b\u4e86\u6700\u76f4\u89c2\u4e14\u53ef\u89c6\u5316\u7684\u7406\u89e3\u65b9\u5f0f\uff0c\u4e5f\u4e3a\u62d3\u5c55\u5230\u9ad8\u7ef4\u7a7a\u95f4\u7684\u53d8\u91cf\u4e0e\u6570\u636e\u63d0\u4f9b\u4e86\u5165\u95e8\u7684\u57fa\u7840\u3002<\/span><\/section>\n

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\u65cb\u8f6c\u6a21\u578b\u76f8\u5173\u5b9e\u9a8c\uff0c\u56f4\u7ed5\u4e00\u6761\u76f4\u7ebf\u8fdb\u884c\u8fd0\u52a8\uff0c\u5e76\u4e14\u6536\u655b\u4e8e\u8be5\u76f4\u7ebf\u65f6\uff0c1\u7ef4\u7684\u5b8f\u89c2\u6001\u662f\u6700\u4f18\u89e3\uff1b\u82e5\u662f\u6536\u655b\u5230\u4e00\u4e2a\u5e73\u9762\uff0c\u90a3\u4e48\u538b\u7f29\u5230\u4e8c\u7ef4\uff0c\u4f1a\u4ea7\u751f\u6700\u5927\u7684\u56e0\u679c\u6d8c\u73b0\u3002<\/span><\/section>\n


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\u968f\u673a\u6e38\u8d70<\/span><\/strong><\/span><\/h4>\n

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\u968f\u673a\u6e38\u8d70\uff0c\u5206\u6790\u4fa7\u91cd\u4e8e\u566a\u58f0\u03b5<\/span>t<\/sub>\u548c\u534f\u65b9\u5dee\u77e9\u9635\u2211<\/span>\uff0c\u5b83\u4eec\u4e3b\u8981\u5f71\u54cd\u786e\u5b9a\u6027\u7684\u51fa\u73b0\u3002\u968f\u673a\u6e38\u8d70\u6a21\u578b\u662f\u4e00\u79cd\u6570\u5b66\u6a21\u578b\uff0c\u7528\u4e8e\u63cf\u8ff0\u7269\u4f53\u5728\u7279\u5b9a\u7a7a\u95f4\u4e2d\u7684\u968f\u673a\u8fd0\u52a8\uff0c\u5176\u4e2d\uff0c\u6b65\u884c\u8005\u5728\u4e00\u7cfb\u5217\u4f4d\u7f6e\u4e4b\u95f4\u79fb\u52a8\uff0c\u6bcf\u6b21\u79fb\u52a8\u7684\u65b9\u5411\u548c\u8ddd\u79bb\u90fd\u662f\u968f\u673a\u7684\u3002\u5728\u7c97\u7c92\u5316\u53c2\u6570\u77e9\u9635W\u7684\u5947\u5f02\u503c\u5747\u4e3a1\u7684\u6761\u4ef6\u4e0b\uff0ck\u8d8a\u5c0f\uff0c\u7cfb\u7edf\u7684\u786e\u5b9a\u6027\u8d8a\u5f3a\uff0c\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u4f1a\u8d8a\u5f3a\u3002<\/span><\/section>\n

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\u968f\u673a\u6e38\u8d70\u76f8\u5173\u5b9e\u9a8c\u7ed3\u679c<\/span><\/section>\n


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\u70ed\u91cf\u8017\u6563<\/span><\/strong><\/span><\/h4>\n

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\u70ed\u91cf\u8017\u6563\u6a21\u578b\u76f8\u5173\u5b9e\u9a8c\u7ed3\u679c<\/span><\/section>\n

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\u968f\u673a\u6e38\u8d70\u4fa7\u91cd\u4e8e\u786e\u5b9a\u6027\u548c\u566a\u58f0\uff0c\u800c\u8017\u6563\u6a21\u578b\u5219\u4fa7\u91cd\u4e8e\u975e\u7b80\u5e76\u6027\u548c\u53c2\u6570\u77e9\u9635A\u3002\u70ed\u91cf\u8017\u6563\u6a21\u578b\u63cf\u8ff0\u4e86\u7cfb\u7edf\u4e0d\u540c\u8282\u70b9\u4e4b\u95f4\u76f8\u4e92\u4f20\u9012\u70ed\u91cf\u7684\u540c\u65f6\uff0c\u5411\u5916\u754c\u73af\u5883\u8017\u6563\u70ed\u91cf\u7684\u6f14\u5316\u6a21\u578b\u3002\u964d\u7ef4\u540ek\u8d8a\u5c0f\uff0c\u7cfb\u7edf\u7684\u7b80\u5e76\u6027\u8d8a\u5f31\uff0c\u6700\u4f18\u7684\u56e0\u679c\u6d8c\u73b0\u7684\u7a0b\u5ea6\u4f1a\u8d8a\u5f3a\u3002<\/span><\/section>\n

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\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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\u5982\u679c\u662f\u8981\u628a\u6a21\u578b\u5199\u6210\u66f4\u4e00\u822c\u7684\u5f62\u5f0f\uff0c\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u5c31\u662f\u63cf\u8ff0\u968f\u673a\u53d8\u91cfxt<\/sub>\u968f\u65f6\u95f4t\u7684\u6f14\u5316\u89c4\u5f8b\u7684\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u9664\u4e86\u5177\u6709\u7279\u5b9a\u7684\u6f14\u5316\u89c4\u5f8b\u4e4b\u5916\uff0c\u8fd8\u5177\u6709\u968f\u673a\u6027\uff0c\u5982\u80a1\u7968\u4ef7\u683c\u3001\u6e29\u5ea6\u53d8\u5316\u3001\u4ea4\u901a\u6d41\u91cf\u3001\u5206\u5b50\u8fd0\u52a8\u7b49\u90fd\u53ef\u4ee5\u7528\u8be5\u6a21\u578b\u5efa\u6a21\u3002\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u5f62\u5982<\/span><\/section>\n

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\u5176\u4e2d<\/sub><\/span>\uff0c\u91cd\u8981\u7279\u5f81\u5219\u662f\u566a\u58f0\u8d8b\u4e8e0\u65f6\uff0c\u4e24\u4e2a\u65f6\u523b\u95f4\u7684\u8fed\u4ee3\u51fd\u6570\u662f\u7ebf\u6027\u51fd\u6570\u3002\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0\u4e0d\u4ec5\u53ef\u4ee5\u7ed9\u51fa\u7ebf\u6027\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u6709\u6548\u4fe1\u606f\u548c\u56e0\u679c\u6d8c\u73b0\u7684\u89e3\u6790\u8868\u8fbe\u5f0f\uff0c\u8fd8\u53ef\u4ee5\u786e\u5b9a\u6700\u4f73\u7ebf\u6027\u7c97\u7c92\u5316\u7b56\u7565\u3002<\/span><\/section>\n

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\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u7c97\u7c92\u5316\u7b56\u7565<\/span><\/strong><\/span><\/h4>\n

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\u5728\u300a\u590d\u6742\u300b\u4e00\u4e66\u4e2d\uff0c\u63d0\u5230\u7684\u7528\u6765\u8de8\u8d8a\u5c42\u7ea7\u5e76\u8f85\u52a9\u7814\u7a76\u4e0d\u540c\u5c42\u7ea7\u89c4\u5f8b\u7684\u201c\u5206\u7c7b\u5668\u201d\uff0c\u5c31\u662f\u7c97\u7c92\u5316\u7b56\u7565\u91cd\u8981\u7684\u5e94\u7528\u9886\u57df\uff0c\u201c\u5206\u7c7b\u5668\u201d\u53ef\u4ee5\u901a\u8fc7\u7c7b\u4f3c\u81ea\u50ac\u5316\u96c6\u7684\u65b9\u5f0f\u8fdb\u884c\u7ec4\u7ec7\u548c\u518d\u7ec4\u7ec7\uff0c\u6587\u7ae0\u4f53\u73b0\u7684\u5c31\u662f\u9488\u5bf9\u67d0\u79cd\u6307\u6807\u5bf9\u7c97\u7c92\u5316\u7b56\u7565\u7684\u4f18\u5316\u3002<\/span><\/section>\n

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\u5bf9\u4e8e\u7ebf\u6027\u8fed\u4ee3\u7cfb\u7edf\uff0c\u6700\u76f4\u89c2\u7684\u64cd\u4f5c\u5c31\u662f\u8fdb\u884c\u964d\u7ef4\u7ebf\u6027\u53d8\u6362\uff0c\u4e5f\u79f0\u6295\u5f71<\/span><\/section>\n

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\u4ece\u800c\u5f97\u5230\u4e00\u4e2a\u5b8f\u89c2\u53d8\u91cf\uff0c\u540c\u65f6\u4e5f\u5f97\u5230\u9488\u5bf9\u5b8f\u89c2\u53d8\u91cf\u7684\u4e00\u4e2a\u65b0\u7684\u968f\u673a\u7ebf\u6027\u8fed\u4ee3\u7cfb\u7edf<\/span><\/section>\n

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\u8fd9\u91cc\u7684\u964d\u7ef4\u77e9\u9635W\u53ef\u88ab\u89c6\u4e3a\u4e00\u79cd\u7c97\u7c92\u5316\u7b56\u7565\u3002\u6211\u4eec\u5728\u5bf9\u53d8\u91cf\u8fdb\u884c\u7c97\u7c92\u5316\u7684\u540c\u65f6\uff0c\u76f8\u5f53\u4e8e\u4e5f\u5bf9\u52a8\u529b\u5b66\u7cfb\u7edf\u505a\u4e86\u7c97\u7c92\u5316\uff0c\u5f97\u5230\u4e86\u6709\u7740\u81ea\u5df1\u7684\u52a8\u529b\u5b66\u53c2\u6570\u548c\u968f\u673a\u566a\u58f0\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u3002<\/span><\/section>\n

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\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u6709\u6548\u4fe1\u606f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


<\/p>\n

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


<\/p>\n

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<\/p>\n

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3. \u7b2c\u4e09\u4e2a\u65b9\u5411\u662f\u91cf\u5316\u548c\u63a2\u7d22EI\u4e0e\u672a\u77e5\u6a21\u578b\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u7cfb\uff0c\u5982\u65f6\u95f4\u5e8f\u5217\u6a21\u578b\u4e0a\u7684\u683c\u5170\u6770\u56e0\u679c\u5173\u7cfb\u3002<\/span><\/section>\n

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\u5e0c\u671b\u5728\u672a\u6765\u80fd\u6709\u66f4\u591a\u7684\u76f8\u5173\u7814\u7a76\uff0c\u6765\u5b8c\u5584\u56e0\u679c\u6d8c\u73b0\u7684\u6846\u67b6\uff0c\u6b22\u8fce\u5927\u5bb6\u7684\u5173\u6ce8\u4e0e\u52a0\u5165\u3002<\/span><\/section>\n

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1. Hoel, E.P.; Albantakis, L.; Tononi, G. Quantifying causal emergence shows that macro can beat micro. Proc. Natl. Acad. Sci. USA<\/em> 2013, 110<\/em>, 19790\u201319795.<\/span><\/p>\n

2. Hoel, E.P. When the map is better than the territory. Entropy<\/em> 2017, 19<\/em>, 188.<\/span><\/p>\n

3. Chvykov, P.; Hoel, E. Causal geometry. Entropy<\/em> 2020, 23<\/em>, 24.<\/span><\/p>\n

4. Zhang, J.; Liu, K. Neural information squeezer for causal emergence. Entropy<\/em> 2022, 25<\/em>, 26.<\/span><\/p>\n

5. Yang, M.; Wang, Z.; Liu, K.; Rong, Y.; Yuan, B.; Zhang, J. Finding emergence in data: Causal emergence inspired dynamics learning. arXiv<\/em> 2023, arXiv:2308.09952.<\/span><\/p>\n

6. Tononi, G.; Sporns, O. “Measuring information integration”. BMC Neuroscience<\/em>. 2003, 4 (31).<\/span><\/p>\n


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\u5728\u96c6\u667a\u4ff1\u4e50\u90e8\u300c\u56e0\u679c\u6d8c\u73b0\u7b2c\u4e94\u5b63\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7855\u58eb\u7814\u7a76\u751f\u5218\u51ef\u5a01\u4ecb\u7ecd\u4e86\u53d1\u8868\u4e8eEntropy\u7684\u8fd9\u9879\u6700\u65b0\u7814\u7a76\u201c\u968f\u673a\u8fed\u4ee3\u7cfb\u7edf\u7684\u56e0\u679c\u6d8c\u73b0<\/span>\u201d\uff0c\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u52a0\u5165\u8bfb\u4e66\u4f1a\u89c2\u770b\u89c6\u9891\u56de\u653e\u3002<\/span><\/section>\n
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Entropy \u6742\u5fd7 Causality and Complex Systems \u7279\u520a\u76ee\u524d\u5728\u6301\u7eed\u5f81\u7a3f\u4e2d\uff0c\u6b22\u8fce\u5bf9\u76f8\u5173\u8bdd\u9898\u611f\u5174\u8da3\u7684\u7814\u7a76\u8005\u6295\u7a3f\uff0c\u4f1a\u8bae\u6587\u7ae0\u4e5f\u53ef\u6295\u7a3f\u3002<\/span><\/p>\n


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\u4e3b\u8981\u4fe1\u606f\u5982\u4e0b\uff1a<\/span><\/p>\n

\u671f\u520a\uff1aEntropy (ISSN 1099-4300)<\/span><\/p>\n

\u680f\u76ee\uff1a\u590d\u6742\u6027\u7279\u520a<\/span><\/p>\n

\u4e3b\u9898\uff1a\u56e0\u679c\u4e0e\u590d\u6742\u7cfb\u7edf\uff08Causality and Complex Systems\uff09<\/span><\/p>\n

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