标题： 随机方法在平衡与非平衡热力学中的应用 显示英文标题

标题： Stochastic approach to equilibrium and nonequilibrium thermodynamics

摘要： 我们基于随机动力学发展了统计热力学的方法，该方法可以是离散的（主方程）或连续的（福克-普朗克方程），并基于关于熵的两个假设。 第一个是熵本身的定义，第二个是熵产生率的定义，该产生率是非负的，并在热力学平衡时为零。 基于这些假设，我们研究了处于平衡或非热力学平衡状态下的多自由度相互作用系统，以及宏观定律如何从随机动力学中推导出来。 这些研究包括准平衡过程、平衡面的凸性、热力学势的时间单调行为（包括熵）、熵产生率的双线性形式、昂萨格系数和倒易关系，以及化学反应的非平衡稳态。 显示英文摘要

摘要： We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second, the definition of entropy production rate which is nonnegative and vanishes in thermodynamic equilibrium. Based on these assumptions we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium, and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasi-equilibrium processes, the convexity of the equilibrium surface, the monotonic time behavior of thermodynamic potentials, including entropy, the bilinear form of the entropy production rate, the Onsager coefficients and reciprocal relations, and the nonequilibrium steady states of chemical reactions.