Derivation of the fundamental equations of continuum thermodynamics from statistical mechanics

TL;DR

This paper derives the fundamental equations of continuum thermodynamics directly from classical statistical mechanics, providing a rigorous link between microscopic particle behavior and macroscopic thermodynamic laws.

Contribution

It offers an exact derivation of continuum thermomechanics equations from statistical mechanics, clarifying the microscopic basis of macroscopic thermodynamic quantities.

Findings

Exact derivation of continuum equations from statistical mechanics

Macroscopic state functions as expected values of microscopic variables

Provides a rigorous theoretical foundation for thermodynamics

Abstract

Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions (density, velocity, stress, energy density, heat flux) are interpreted as expected values.