Exact equation for classical many-particle systems in closed form: from mechanics to statistical thermodynamics

TL;DR

This paper derives exact, closed-form equations for classical many-particle systems, linking microscopic dynamics to thermodynamics without statistical assumptions, and explores implications for equilibrium and wave phenomena.

Contribution

It provides the first exact, assumption-free equations for many-particle systems, connecting microscopic mechanics to thermodynamics and wave behavior.

Findings

Derived exact equations of motion for particle density.

Established integral equations for equilibrium distributions.

Connected inter-particle potentials to sound dispersion laws.

Abstract

The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the particles is deduced. No statistical or probabilistic hypotheses and assumption in these deductions have been used. Some well known results of equilibrium statistical mechanics are deduced from the obtained equations as simple limiting cases. The wave equation for almost homogeneous systems with inter-particle interactions are obtained. Connection between inter-particle potential and dispersion law of sound is established. Keywords: Many-body systems dynamics; inter-atomic potentials; phase equilibrium PACS 05.20.-y; 05.10.-a; 05.70.Ln