Statistical Principles of Elastic Particles in Digital Phase Space

Abstract

Zhong-Cheng Liang

By introducing the path subspace, this study extends the energy phase space to a digital phase space (�?-space), thus accomplishing the numerical statistics of the elastic particle equilibrium systems. Unlike the �? -space (6N dimensions) of Gibbs statistical ensemble, the �?-space (18N dimensions) is divided into three areas: liquid, solid, and gas, and their energy probability distributions have cyclic symmetry. The interaction between particles in �?- space is characterized by the degree of association/dissociation, thereby avoiding the problem of potential energy integration in �?-space. This article presents the macroscopic and mesoscopic equilibrium conditions for elastic particle systems and derives the partition functions and state functions for three areas. In addition, the differential equations of thermodynamics are generalized to the entire range of matter states by extending the definition of the entropy function. The results show that the states and changes of the thermodynamic system can be completely expressed by five independent parameters (two digits and three scales), and the first and second laws of thermodynamics can also be naturally derived from the statistical theory of digital phase space.

PDF