Thermodynamics within the Framework of Classical Mechanics

TL;DR

This paper offers a theoretical framework linking classical mechanics to thermodynamics by analyzing a non-equilibrium conservative system split into subsystems, deriving equations that explain irreversibility and entropy production.

Contribution

It introduces a generalized Liouville equation and demonstrates the non-potential nature of subsystem interactions, providing a new mechanism for irreversibility within classical mechanics.

Findings

Derived a generalized Liouville equation for subsystems

Identified conditions for irreversibility based on interaction forces

Established a formula relating entropy to subsystem forces

Abstract

The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in equilibrium. Based on the D'Alambert equation for a subsystem the generalized Liouville equation is obtained. A necessary condition for irreversibility is determined. This condition is dependence the forces of interaction of subsystems on relative velocities. The equation of motion of subsystems of potentially interacting elements is obtained. The non-potentiality of the forces of interaction of the subsystems consisting of potentially interacting elements is proved. The mechanism of occurrence of irreversible dynamics is offered. The formula that expresses the entropy through the forces of interaction of subsystems is obtained. The theoretical link between classical mechanics and thermodynamics is analyzed.