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PC\uff09\uff0c\u5c31\u66f4\u52a0\u7406\u60f3\u5316\u4e86\u2014\u2014\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e48\u70eb\u7684\u4e1c\u897f\u653e\u5728\u819d\u76d6\u4e0a\u6700\u591a\u4e0d\u8d85\u8fc7\u4e09\u5206\u949f\u5c31\u53d7\u4e0d\u4e86\u4e86\uff0c\u7cfb\u7edf\u6bd4\u8f83\u6162\u7684\u4e09\u5206\u949f\u8fd8\u4e0d\u591f\u5f00\u673a\u2026\u2026\u3002 \u8ba1\u7b97\u673a\u7684\u6563\u70ed\u95ee\u9898\u4e00\u76f4\u662f\u4e00\u4e2a\u8001\u5927\u96be\u3002\u7535\u8111\u91cc\u9762\u5f88\u591a\u5143\u4ef6\u90fd\u4f1a\u5f88\u70eb\uff0c\u62c6\u8fc7\u7535\u8111\u7684\u5c31\u77e5\u9053\uff0c\u6700\u70eb\u7684\u5730\u65b9\u90fd\u662f\u786c\u76d8\u548c\u82af\u7247\u2014\u2014\u4fe1\u606f\u5904\u7406\u7684\u4e2d\u5fc3\u3002\u82af\u7247\u4e4b\u6240\u4ee5\u53d1\u70ed\uff0c\u662f\u56e0\u4e3a\u4fe1\u606f\u5904\u7406\u7684\u7269\u7406\u5b9e\u73b0\u662f\u4e0d\u53ef\u9006\u8fc7\u7a0b\uff0c\u6839\u636e\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\uff0c\u5c31\u8981\u4ea7\u751f\u4e00\u5b9a\u7684\u70ed\u91cf\u3002\u70ed\u529b\u5b66\u7684\u8868\u8ff0\u6709\u5f88\u591a\u79cd\uff0c\u5168\u90fd\u542c\u7740\u4ee4\u4eba\u6cae\u4e27\u3002\u5728\u5386\u53f2\u4e0a\u540c\u6837\u8ba8\u538c\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u8457\u540d\u5386\u53f2\u5b66\u5bb6\u662f\u9ea6\u514b\u65af\u97e6\uff08James Clerk Maxwell\uff09\uff0c\u4e3a\u4e86\u7ed9\u7b2c\u4e8c\u5b9a\u5f8b\u627e\u832c\u513f\uff0c\u4ed6\u57281867\u5e74\u63d0\u51fa\u4e86\u4e00\u79cd\u60c5\u51b5\uff1a \u4e00\u4e2a\u88c5\u6709\u6c14\u4f53\u7684\u5c01\u95ed\u7edd\u70ed\u5bb9\u5668\u4e2d\u95f4\u6709\u4e00\u4e2a\u6863\u677f\u628a\u5bb9\u5668\u5206\u6210A\u3001B\u5de6\u53f3\u4e24\u5ba4\u3002\u6863\u677f\u539f\u672c\u662f\u6253\u5f00\u7684\uff0c\u4e8e\u662f\u6574\u4e2a\u5bb9\u5668\u8fbe\u5230\u4e86\u5e73\u8861\u3002\u5047\u5982\u6709\u4e00\u4e2a\u5c0f\u7cbe\u7075\u64cd\u7eb5\u6863\u7248\u5728\u65c1\u8fb9\u770b\u7740\u8fd9\u4e9b\u6c14\u4f53\u5206\u5b50\uff0c\u628a\u5176\u4e2d\u8dd1\u5f97\u5feb\u7684\u653e\u5230\u5de6\u8fb9\u53bb\uff0c\u8dd1\u5f97\u6162\u7684\u653e\u5230\u53f3\u8fb9\u53bb\uff0c\u8fd9\u6863\u677f\u662f\u7406\u60f3\u7684\uff0c\u6ca1\u6709\u78e8\u64e6\uff0c\u4e8e\u662f\u8fd9\u5c0f\u7cbe\u7075\u5c3d\u7ba1\u6765\u6765\u56de\u56de\u5730\u5fd9\u6d3b\u4f46\u662f\u505a\u529f\u4e3a\u96f6\u3002\u8fd9\u6837\u7684\u8bdd\uff0c\u6700\u7ec8\u4f53\u7cfb\u5c31\u53d8\u6210\u4e00\u8fb9\u51b7\u4e00\u8fb9\u70ed\u4e86\u3002 \u8fd9\u4e2a\u601d\u60f3\u5b9e\u9a8c\u6700\u5148\u662f\u5728\u9ea6\u514b\u65af\u97e6\u7684\u4e66\u300aTheory of Heat\u300b\u7684\u672b\u7ae0Limitation of the Second Law of Thermodynamics\u3002\u540e\u6765\u5a01\u5ec9\u00b7\u6c64\u59c6\u68ee\uff08\u5c31\u662f\u5f00\u5c14\u6587\u7235\u58eb\uff09\u628a\u8fd9\u4e2a\u5c0f\u7cbe\u7075\u79f0\u4f5c\u201c\u9ea6\u514b\u65af\u97e6\u5996\u201d\uff08Maxwell's Demon\uff09\u3002\u6309\u7167\u9ea6\u514b\u65af\u97e6\u5996\u7684\u80fd\u529b\uff0c\u5b83\u4e5f\u53ef\u4ee5\u628a\u6df7\u5300\u4e86\u7684\u5316\u5408\u7269\u91cd\u65b0\u5206\u6210\u7eaf\u7269\u8d28\u800c\u4e0d\u4f5c\u529f\uff0c\u628a\u81a8\u80c0\u4e86\u7684\u6c14\u4f53\u91cd\u65b0\u538b\u7f29\u800c\u4e0d\u505a\u529f\u2026\u2026\u4efb\u4f55\u4e00\u4e2a\u4f8b\u5b50\u90fd\u8db3\u4ee5\u63a8\u7ffb\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u3002 \u53ea\u8981\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u5931\u6548\uff0c\u6211\u4eec\u5c31\u6709\u671b\u4e0d\u7528\u505a\u529f\u6765\u7ef4\u6301\u4f4e\u71b5\u6709\u5e8f\uff0c\u5c31\u6709\u671b\u8bbe\u8ba1\u51fa\u4e0d\u7528\u80fd\u8017\uff0c\u4e0d\u751f\u70ed\u7684\u8ba1\u7b97\u673a\u6765\u3002\u6211\u4eec\u771f\u80fd\u8bf7\u9ea6\u514b\u65af\u97e6\u5996\u6765\u7ed9\u6211\u4eec\u7684\u7b14\u8bb0\u672c\u7535\u8111\u6563\u70ed\u5417\uff1f 1929\u5e74L. Szilard\u5728\u53d1\u8868\u4e86\u4e00\u7bc7\u8457\u540d\u7684\u53cd\u9a73\u9ea6\u514b\u65af\u97e6\u5996\u7684\u6587\u7ae0\uff08Zeitschrift f\u00fcr Physik A: Hadrons and Nuclei, 1929, 53, 840-856. DOI: 10.1007\/BF01341281\uff09\u3002\u4ed6\u8ba4\u4e3a\uff0c\u9ea6\u514b\u65af\u97e6\u5996\u5fc5\u987b\u901a\u8fc7\u67d0\u79cd\u5f62\u5f0f\u7684\u6d4b\u91cf\u624d\u80fd\u77e5\u9053\u54ea\u4e2a\u5206\u5b50\u8dd1\u5f97\u5feb\uff0c\u54ea\u4e2a\u5206\u5b50\u8dd1\u5f97\u6162\u3002\u8fd9\u4e2a\u6d4b\u91cf\u7684\u8fc7\u7a0b\uff0c\u4ee5\u53ca\u4fe1\u606f\u7684\u83b7\u5f97\uff0c\u5fc5\u7136\u8981\u5bfc\u81f4\u71b5\u589e\u3002\u6240\u4ee5\uff0c\u5bb9\u5668\u5185\u7684\u6c14\u4f53\u81ea\u52a8\u53d8\u6210\u4e00\u8fb9\u51b7\u4e00\u8fb9\u70ed\u7684\u8fc7\u7a0b\u7684\u71b5\u964d\uff0c\u90fd\u88ab\u9ea6\u514b\u65af\u97e6\u5996\u4e0d\u65ad\u64cd\u5fc3\u7684\u71b5\u589e\u7ed9\u62b5\u6d88\u6389\u4e86\u3002 \u6807\u9898\u7684\u82f1\u8bed\u7ffb\u8bd1\u662f\uff1aOn the entropy reduction in a thermodynamic system with intelligent beings interference\uff08\u8bba\u667a\u6167\u751f\u7269\u5e72\u6270\u4e0b\u7684\u71b5\u51cf\u4f53\u7cfb\uff09 \u8fd9\u8bf4\u660e\uff0c\u201c\u64cd\u5fc3\u201d\u4e5f\u5c5e\u4e8e\u505a\u529f\u7684\u4e00\u79cd\uff01\u9ea6\u514b\u65af\u97e6\u5996\u7eaf\u64cd\u5fc3\u4e5f\u8981\u51fa\u6c57\uff0c\u8981\u751f\u70ed\u7684\uff0c\u6240\u4ee5\uff0c\u8bf7\u9ea6\u514b\u65af\u97e6\u5996\u6765\u7ed9\u7b14\u8bb0\u672c\u6563\u70ed\u7684\u4e3b\u610f\u57fa\u672c\u4e0a\u6ca1\u620f\u3002 \u5173\u4e8e\u8fd9\u4e2a\u95ee\u9898\uff0c\u8ba1\u7b97\u673a\u5de8\u5934IBM\u4e5f\u6ca1\u5c11\u64cd\u5fc3\u8fc7\uff08\u71b5\u4e5f\u589e\u4e86\u4e0d\u5c11\uff09\uff0c1961\u5e74\uff0cIBM\u7684\u7814\u7a76\u4eba\u5458Rolf Landauer\u5728IBM Journal of Research and Development\u53d1\u8868\u4e86\u4e00\u7bc7\u6587\u7ae0\uff0c\u8bc1\u660e\u4e86\u6bcf\u6bd4\u7279\u4fe1\u606f\u7684\u4e0d\u53ef\u9006\u64cd\u4f5c\u6700\u5c11\u8981\u589e\u52a0\u5927\u5c0f\u4e3akBln2\u7684\u71b5\uff0c\u5176\u4e2dkB\u662f\u73bb\u5c14\u5179\u66fc\u5e38\u6570\u3002\u5f88\u591a\u4fe1\u606f\u5904\u7406\u90fd\u662f\u4e0d\u53ef\u9006\u64cd\u4f5c\uff0c\u6bd4\u5982\u5bf9\u4e24\u6bd4\u7279\u7684\u5f02\u6216\u64cd\u4f5c\uff0c\u56e0\u4e3a\u53ea\u6709\u4e00\u6bd4\u7279\u7684\u8f93\u51fa\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u635f\u5931\u4e86\u4e00\u4e2a\u81ea\u7531\u5ea6\uff0c\u56e0\u6b64\u662f\u4e0d\u53ef\u9006\u7684\u3002\u8fd9\u5c31\u8ba9\u5927\u5bb6\u5174\u594b\u4e86\u2014\u2014\u5982\u679c\u628a\u4fe1\u606f\u7684\u903b\u8f91\u5904\u7406\u90fd\u6539\u6210\u53ef\u9006\u8fc7\u7a0b\uff0c\u5c31\u53ef\u4ee5\u8fbe\u5230\u65e0\u71b5\u589e\u7684\u4fe1\u606f\u5904\u7406\uff08\u6216\u8005\u8bf4\u4fe1\u606f\u71b5\u4e3a\u96f6\uff09\u5462\uff1f\u5f88\u591a\u903b\u8f91\u5904\u7406\u90fd\u53ef\u4ee5\u8bbe\u8ba1\u6210\u53ef\u9006\u7684\uff0c1972\u5e74\uff0cIBM\u7684\u53e6\u4e00\u4e2a\u7814\u7a76\u5458Bennett\u751a\u81f3\u8bc1\u660e\u4e86\u6240\u6709\u8ba1\u7b97\u90fd\u80fd\u627e\u5230\u4e00\u4e2a\u53ef\u9006\u7684\u903b\u8f91\u8def\u5f84\u3002\u56e0\u6b64\uff0c\u79d1\u5b66\u5bb6\u5c31\u5f00\u59cb\u7814\u7a76\u201c\u53ef\u9006\u8ba1\u7b97\u201d\uff08reversible\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","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":9108,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9108","url_meta":{"origin":1799,"position":5},"title":"Leon B. Lucy","author":"Andrew","date":"2024\u5e7412\u670814\u65e5","format":false,"excerpt":"[latexpage] \u80cc\u666f \u5728\u6570\u503c\u8ba1\u7b97\u9886\u57df\u6709\u4e00\u4e2a\u6bd4\u8f83\u77e5\u540d\u7684\u53bb\u5377\u79ef\u8fed\u4ee3\u7b97\u6cd5\u2014\u2014Lucy--Richardson\u7b97\u6cd5\uff0c\u5b83\u88ab\u540e\u4e16\u96c6\u4e2d\u7528\u4e8e\u56fe\u50cf\u53bb\u566a\u3002\u4f8b\u5982\uff0cMATLAB\u7684Image Processing Toolbox\u6709\u4e00\u4e2adeconvlucy\u547d\u4ee4\uff0c\u58f0\u79f0\u5c31\u662f\u7528Lucy--Richardson\u7b97\u6cd5\u5bf9\u7ed9\u5b9a\u56fe\u7247\uff08\u50cf\u7d20\u77e9\u9635\uff09\u4f5c\u7ed9\u5b9a\u70b9\u6269\u6563\u51fd\u6570\u7684\u53bb\u566a\u3002 \u4f46\u662f\uff0cLucy\u7684\u539f\u6587\u6240\u9488\u5bf9\u7684\u95ee\u9898\uff0c\u6bd4\u73b0\u5728\u4e00\u822c\u5e94\u7528\u66f4\u5e7f\u4e49\u3002\u5047\u5b9a$X$\u662f\u4e00\u4e2a\u8fde\u7eed\u53d6\u503c\u968f\u673a\u53d8\u91cf\u3002\u5b83\u7406\u5e94\u6309\u7167\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570$\\phi\\left(x\\right)$\u3002\u6211\u4eec\u60f3\u628a$\\phi\\left(x\\right)$\u89c6\u4e3a\u67d0\u79cd\u7b80\u5355\u5206\u5e03$P\\left(x\\middle|\\xi\\right)$\u6309\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u7684\u53e0\u52a0\u7ed3\u679c\uff1a \\begin{equation}\\label{eq:original_phi_expression}\\phi\\left(x\\right)=\\int P\\left(x\\middle|\\xi\\right)\\psi\\left(\\xi\\right)\\mathrm{d}\\xi\\end{equation} \u800c\u6211\u4eec\u60f3\u5f97\u77e5\u7ed9\u5b9a\u5f62\u5f0f\u7684\u6838$P\\left(x\\middle|\\xi\\right)$\u6240\u5bf9\u5e94\u7684\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u3002\u5728\u8fd9\u91cc\uff0c$\\xi$\u662f\u6838\u51fd\u6570$P$\u7684\u53c2\u6570\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u5173\u5fc3\u9ad8\u65af\u6838\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u90a3\u4e48$P\\left(x\\middle|\\xi\\right)$\u53ef\u80fd\u662f\u4ee5$\\xi$\u4e3a\u6807\u51c6\u5dee\u7684\u9ad8\u65af\u51fd\u6570 \\[P\\left(x\\middle|\\xi\\right)=\\frac{1}{\\sqrt{2\\pi\\xi^2}}\\exp\\left[-\\frac{\\left(x-\\mu\\right)^2}{2\\xi^2}\\right]\\] \u5728\u56fe\u50cf\u53bb\u566a\u7684\u4e0a\u4e0b\u6587\u4e2d\uff0c\u4ee5deconvlucy\u4e3a\u4f8b\uff0c\u6838\u51fd\u6570$P\\left(x\\right)$\u662f\u4e00\u4e2a\u56fa\u5b9a\u53c2\u6570$\\xi$\u7684\u51fd\u6570\uff0c\u4e14$\\xi$\u7684\u53d6\u503c\u8303\u56f4\uff08\u5373$P\\left(x\\right)$\u7684\u201c\u5bbd\u5ea6\u201d\uff09\u8fdc\u7a84\u4e8e$x$\u7684\u8303\u56f4\uff08\u5728\u56fe\u50cf\u8bed\u5883\u4e2d\u662f\u56fe\u50cf\u7684\u5927\u5c0f\uff09\u3002\u4f46\u5728Lucy\u539f\u6587\u7684\u8bed\u5883\u4e2d\uff0c$\\phi\\left(x\\right)$\u3001$P\\left(x\\middle|\\xi\\right)$\u548c$\\psi\\left(\\xi\\right)$\u90fd\u662f\u652f\u6491\u4e3a\u6574\u4e2a\u5b9e\u6570\u7684\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570\u3002\u53ef\u4ee5\u8bf4\uff0c\u56fe\u50cf\u53bb\u566a\u5e94\u7528\uff0c\u53ea\u662fLucy\u539f\u6587\u7b97\u6cd5\u7684\u5176\u4e2d\u4e00\u4e2a\u5f88\u7279\u6b8a\u7684\u4f8b\u5b50\u3002 \u6570\u503c\u8ba1\u7b97\u7684\u8bbe\u8ba1\u827a\u672f 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