统计物理的微观动力学基础

统计的基本出发点是研究系统具有的随机性,不同系统在不同情形下的宏观热力学性质起源于系统内部随机性的差异,通过对宏观热力学系统的微观非线性动力学进行研究探索，我们可以进一步更为深入地理解物态方程、相变等诸多的宏观热力学现象。本文通过哈密顿系统的非线性动力学研究，以及遍历性理论的动力学随机性研究对此问题进行了分析，研究表明，动力学系统的全局性混沌是系统统计成立的根本要素，系统的无限大自由度（热力学极限）已不是决定性的因素，人们可以在此基础上建立少自由度系统的统计力学及热力学。

On the microscopic dynamical foundation of statistical mechanics

The basic starting point of statistics is the stochasticity of the underlying system. Macroscopic thermodynamic properties of different systems under different situations is originated from the diversity in the intrinsic stochasticity of these systems. Based on an exhaustive exploration of microscopic nonlinear dynamics of thermodynamic system,one can get a deeper understanding of a number of thermodynamic phenomena such as matter-state equations and phase transitions. In this paper, nonlinear dynamics of Hamiltonian systems and dynamical stochasticity in ergodic theory are analyzed. Our analysis indicates that global chaos is the essence for the validity of statistics. Infinite numbers of degrees of freedom and thermodynamic limit are not the decisive criterion for statistics. In torms of this few-body statistical mechanics and thermodynamics can be built.