A Generalization of Onsager’s Reciprocity Relations to Gradient Flows with Nonlinear Mobility

Abstract

AbstractOnsager’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.