Thermodynamic entropy as a Noether invariant in a Langevin equation

TL;DR

This paper demonstrates that thermodynamic entropy can be derived as a Noether invariant in a stochastic Langevin process, revealing a symmetry-based foundation for entropy in thermodynamics.

Contribution

It introduces a novel connection between thermodynamic entropy and Noether invariants within the framework of Langevin equations and stochastic processes.

Findings

Entropy emerges as a Noether invariant in quasi-static Langevin processes.

The Martin-Siggia-Rose-Janssen-de Dominicis action exhibits a continuous symmetry.

Symmetry analysis links thermodynamic entropy to fundamental invariants.

Abstract

We study the thermodynamic entropy as a Noether invariant in a stochastic process. Following the Onsager theory, we consider the Langevin equation for a thermodynamic variable in a thermally isolated system. By analyzing the Martin-Siggia-Rose-Janssen-de Dominicis action of the Langevin equation, we find that this action possesses a continuous symmetry in quasi-static processes, which leads to the thermodynamic entropy as the Noether invariant for the symmetry.