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.

arXiv comment12 pages, 2 figures

References in corpus (15)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Equality connecting energy dissipation with violation of fluctuation-response relation
• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Energy dissipation and violation of the fluctuation-response relation in non-equilibrium Langevin systems
• Thermodynamic entropy as a Noether invariant
• Spontaneous symmetry breaking and Nambu-Goldstone modes in dissipative systems
• Dispersion relations of Nambu-Goldstone modes at finite temperature and density
• Dynamical symmetries of Markov processes with multiplicative white noise
• (Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional
• Emergent Supersymmetry in Local Equilibrium Systems
• Thermodynamical path integral and emergent symmetry

Cited by in corpus (6)

• Why Noether's Theorem applies to Statistical Mechanics
• Noether-Constrained Correlations in Equilibrium Liquids
• Variance of fluctuations from Noether invariance
• First part of Clausius heat theorem in terms of Noether's theorem
• Entropy as Noether charge for quasistatic gradient flow
• Noether's theorem applied to GENERIC