Entropy as Noether charge for quasistatic gradient flow

TL;DR

This paper links entropy increase to broken time-reversal symmetry by extending the symmetry to a continuous one using thermodynamic forces, showing entropy as a Noether charge in quasistatic gradient flows.

Contribution

It introduces a novel framework connecting entropy as a Noether charge to continuous symmetries in quasistatic gradient flows, expanding the understanding of thermodynamic invariance.

Findings

Entropy increase relates to broken time-reversal symmetry.

Entropy as a Noether charge in gradient flow dynamics.

Adiabatic invariance of entropy connects to Noether's theorem.

Abstract

Entropy increase is fundamentally related to the breaking of time-reversal symmetry. By adding the 'extra dimension' associated with thermodynamic forces, we extend that discrete symmetry to a continuous symmetry for the dynamical fluctuations around (nonlinear) gradient flow. The latter connects macroscopic equilibrium conditions upon introducing a quasistatic protocol of control parameters. The entropy state function becomes the Noether charge. As a result, and following ideas expressed by Shin-ichi Sasa and co-workers, the adiabatic invariance of the entropy, part of the Clausius heat theorem, gets connected with the Noether theorem.