Expansion of a Formalism of Classical Mechanics for Nonequilibrium Systems

TL;DR

This paper extends classical Hamiltonian formalism to better describe nonequilibrium systems by constructing a new framework based on equilibrium subsystem dynamics, removing previous restrictions on subsystem forces.

Contribution

It introduces a modified formalism of Lagrange, Hamilton, and Liouville equations tailored for nonequilibrium systems, linking subsystem interactions with thermodynamic energy principles.

Findings

Modified Hamiltonian and Lagrangian equations for nonequilibrium systems

Removal of restrictions on subsystem force dynamics

Connection established between subsystem interaction equations and thermodynamics

Abstract

The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium subsystems by which the nonequilibrium system is represented. It has allowed removing restrictions on dynamics of the subsystems, which dictated by the requirement of monogenic and potentiality of the forces between subsystems. Modified Lagrange, Hamilton and Liouville equations are obtained. Some features of dynamics of nonequilibrium systems are considered. Connection between the equation of interaction of subsystems and a thermodynamic principle of energy is analyzed.