Seeing maximum entropy from the principle of virtual work

TL;DR

This paper extends the principle of virtual work to stochastic systems, linking mechanical equilibrium to maximum entropy, and proposes it as a fundamental law of physics.

Contribution

It introduces a novel mechanical framework that derives maximum entropy as a consequence of virtual work principles, bridging mechanics and thermodynamics.

Findings

Establishes a mechanical basis for maximum entropy in thermodynamics.

Shows the ensemble average of virtual work leads to thermodynamic equilibrium.

Connects principles of mechanics with statistical mechanics.

Abstract

We propose an extension of the principle of virtual work of mechanics to random dynamics of mechanical systems. The total virtual work of the interacting forces and inertial forces on every particle of the system is calculated by considering the motion of each particle. Then according to the principle of Lagrange-d'Alembert for dynamical equilibrium, the vanishing ensemble average of the virtual work gives rise to the thermodynamic equilibrium state with maximization of thermodynamic entropy. This approach establishes a close relationship between the maximum entropy approach for statistical mechanics and a fundamental principle of mechanics, and constitutes an attempt to give the maximum entropy approach, considered by many as only an inference principle based on the subjectivity of probability and entropy, the status of fundamental physics law.