Fokker-Planck方程的推导及其熵产生

中文摘要 AI 辅助

我们从主方程推导出Fokker-Planck方程及其熵产生。为此，我们考虑一个离散的状态空间，其中定义了主方程，并引入了适当的转移速率。转移速率由两部分组成，一部分是与间距倒数成正比的一般项，另一部分与间距平方的倒数成正比，对应于独立随机变量的方差。在连续空间极限下，我们得到了Fokker-Planck方程以及熵产生率和熵通量。我们还考虑了状态空间为相空间的情况，并讨论了适用于与多个热库接触的系统以及孤立系统的方程。

英文摘要

We derive the Fokker-Planck equation and its entropy production from the master equation. To this end we consider a discrete space of states where the master equation is defined and appropriate transition rates are introduced. A transition rate has two parts, one of which is the ordinary term proportional to the inverse of the spacing and the other is inversely proportional to the square of the spacing corresponding to the variance of the independent stochastic variable. In the continuous space limit, we obtain the Fokker-Planck as well as the rate of entropy production and the flux of entropy. We also consider the case where the space of states is the phase space and discuss the equations appropriate for systems in contact with several heat reservoirs and for isolated systems.

发表机构

• Universidade de São Paulo（圣保罗大学）

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