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摘要翻译：
研究了主方程描述的物理化学随机过程。本文研究了主方程和相应的Fokker-Planck方程的熵产生。对于主方程，Gaspard最近利用Kolmogorov-Sinai熵导出了熵产生的精确表达式（{\em J.stat.phys.},\textbf{117}（2004）,599；[勘误表；\textbf{126}（2006）,1109])。虽然Gaspard的表达式是从随机考虑导出的，但应该注意，Gaspard的表达式与热力学表达式是一致的。对于相应的Fokker-Planck方程，利用Onsger-Machlup理论推导涨落定理过程中出现的详细的不平衡关系，用Tomita和Tomita（{\em prog.theor.phys.},\textbf{51}（1974）,1731）提出的{\em涨落的不可逆循环}来表示熵产。然而，对应的Fokker-Planck方程的这一表达式与主方程的熵产生的表达式不同。这种差异是由于主方程与相应的Fokker-Planck方程之间的差异，即前者处理离散事件，而后者是前者的近似。实际上，在后一个方程中，原来的离散事件被平滑掉了。为了克服这一困难，我们提出了{\em路径权重原理}。利用这一原理，修正后的Fokker-Planck方程的熵产率表达式与简单化学反应系统和扩散系统的主方程的熵产率表达式（即热力学表达式）相一致。
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英文标题：
《Irreversible Circulation of Fluctuation and Entropy Production》
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作者：
Hiroyuki Tomita and Mitsusada M. Sano
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Physical and chemical stochastic processes described by the master equation are investigated. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master equation, the exact expression of the entropy production was recently derived by Gaspard using the Kolmogorov-Sinai entropy ({\em J.Stat.Phys.}, \textbf{117} (2004), 599; [Errata; \textbf{126} (2006), 1109 ]). Although Gaspard's expression is derived from a stochastic consideration, it should be noted that Gaspard's expression conincides with the thermodynamical expression. For the corresponding Fokker-Planck equation, by using the detailed imbalance relation which appears in the derivation process of the fluctuation theorem through the Onsger-Machlup theory, the entropy production is expressed in terms of the {\em irreversible circulation of fluctuation}, which was proposed by Tomita and Tomita ({\em Prog.Theor.Phys.}, \textbf{51} (1974), 1731). However, this expression for the corresponding Fokker-Planck equation differs from that of the entropy production for the master equation. This discrepancy is due to the difference between the master equation and the corresponding Fokker-Planck equation, namely the former treats discrete events, but the latter equation is an approximation of the former one. In fact, in the latter equation, the original discrete events are smoothed out. To overcome this difficulty, we propose the {\em path weight principle}. By using this principle, the modified expression of the entropy production for the corresponding Fokker-Planck equation coincides with that of the master equation (i.e., the thermodynamical expression) for a simple chemical reaction system and a diffusion system.
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PDF链接：
https://arxiv.org/pdf/711.2323
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