基于新广义变分原理的非平衡统计力学方法及应用

Non-equilibrium Statistical Mechanics and Applications Based on New Generalized Variational Principle

在近年来非平衡统计力学研究进展的基础上,尝试从广义变分法的视角建立一套描述非平衡统计力学的新方法。即以对哈密顿原理进行修正得到的最大流原理为基础,对开放的复杂系统建立新的统计系综,构造出新的势函数,并推导出随机动力学方程,进而得出重整化方程并进行求解,得到自相似的分形结构,从而建立起一个新的统计力学理论框架。以城市系统为例,结合自组织特征映射网络进行结构模式数值分析,展示了新方法处理复杂系统的强大潜力。

The recent progresses in non-equilibrium statistical mechanics are summarized and an attempt is made to build a new descriptive method based on a new variational principle. By employing Maximum Flux Principle, as modified Hamilton principle for open systems, a new statistical ensemble is developed and a new potential function is defined. Then the Langevin equation and the renormalization equation are obtained, through which the fractal structure is ultimately derived. A new framework of statistical mechanics is therefore outlined. With an example of quantitative analysis of urban system, it shows advantages and potentialities in dealing with universal open complex systems.