Abstract: 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.

Key words: stochasticity, dynamical systems, chaos, ergodicity