Statistical mechanics and fluid structure

Abstract

In the axiomatic approach to the derivation of statistical mechanics the theory is based upon the equations of motions of classical mechanics (Hamilton equations). Since these equations are unstable with respect to initial conditions, in the time τ ≈ 10⁻¹² s they generate chaos in the system of atoms and molecules. This chaos can be described by only probability theory laws. The laws of this theory are introduced into statistical mechanics as the second postulate. However, for both postulates (i.e., Hamilton equations and probability theory laws) to be compatible with each other, about one and a half ten of additional requirements defining in detail the matter model underlying the theory must be imposed on the system. This report analyzes only the restrictions imposed by probability theory. The main of them are: a transition to the thermodynamic limit, the condition of correlation attenuation, and a short-range character of the interaction potential. The matter model formulated based on these restrictions is a continuous medium in which a correlation sphere with a small radius R ≈ 10⁻⁷ cm (physical point) is submerged. It is submerged in an infinite thermostat, the particles of which behave as the ideal gas relative to the particles forming the correlation sphere. Here all macroscopic parameters of matter in this physical point are determined by the state of the correlation sphere. Thus formulated model determines the macro- and microscopic structure of matter, and finally, results in thermodynamic and hydrodynamic equations.