A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility

TL;DR

This paper extends Onsager's reciprocity relations to a broader class of gradient flows with nonlinear mobility, connecting microscopic reversibility to generalized macroscopic evolution equations beyond near-equilibrium conditions.

Contribution

The authors generalize Onsager's reciprocity relations to nonlinear gradient flows, relaxing the assumptions of near-equilibrium and Gaussian invariant measures.

Findings

Derived generalized symmetry conditions for nonlinear gradient flows

Extended the variational characterization of macroscopic evolution equations

Connected microscopic reversibility to a broader class of macroscopic dynamics

Abstract

Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest-ascent, or maximal-entropy-production equation. Onsager's original theorem is limited to close-to-equilibrium situations, with a Gaussian invariant measure and a linear macroscopic evolution. In this paper we generalize this result beyond these limitations, and show how the microscopic time-reversibility leads to natural generalized symmetry conditions, which take the form of generalized gradient flows.