非平衡系统的势函数理论

POTENTIAL FOR NONEQUILIBRIUM SYSTEMS

势函数是在平衡态统计物理中应用得十分成功的理论，将势函数理论推广到非平衡系统是非平衡态统计物理的一项十分重要的任务。本文综述了非平衡态势函数理论的一个重要方面，即利用对随机过程的研究来建立系统的势函数，本文阐述了非平衡系统势函数的定义和概念；论证势函数在系统演化过程中的单调性质；详细介绍了各种计算非平衡势函数的方法；同时介绍了利用势函数解析地研究在噪声作用下的非线性系统的非定态演化行为。整个研究包含了一维和多维系统的广泛系统。

Potential theory has been successfully used for equilibrium systems. It is of great interest to extend the potential theory to nonequilibrium systems. In this review paper the potential theory is established by considering stochastic processes. We elucidate the definition and concept of a nonequilibrium potential,rigorously prove the monotonous evolution of the potential,show in detail various ways in computing this potential,and apply the potential theory in calculation of the initial value problem of nonlinear stochas-tic systems.All investigation includes one-dimensional and multi-dimensional systems.