Thermodynamic entropy as a Noether invariant in a Langevin equation

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.

12 pages, 2 figures

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• Thermodynamic uncertainty relation for biomolecular processes
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Thermodynamical path integral and emergent symmetry