A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility
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.
Keywords
Cite
@article{arxiv.1510.06219,
title = {A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility},
author = {A. Mielke and M. A. Peletier and D. R. M. Renger},
journal= {arXiv preprint arXiv:1510.06219},
year = {2018}
}
Comments
8 pages; contribution to the proceedings of IWNET 2015; this is the author version after taking into account reviewer's comments