Lagrange equations coupled to a thermal equation: mechanics as consequence of thermodynamics

TL;DR

This paper derives coupled mechanical and thermal evolution equations for a closed system of particles, showing how viscous friction links thermodynamics and mechanics, with applications to harmonic interactions.

Contribution

It introduces a novel coupled differential equation framework connecting thermodynamics and mechanics based on Stueckelberg's approach.

Findings

Coupled equations describe thermal and mechanical evolution.

Viscous friction acts as the coupling mechanism.

Application to harmonic particle systems demonstrates the theory.

Abstract

Following the analytic approach to thermodynamics developed by Stueckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction term. Finally, we apply our coupled evolution equations to study the thermodynamics of an isolated system consisting of identical point particles interacting through a harmonic potential.