中文摘要：

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。即以对哈密谊原垂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。

英文摘要：

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.