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arXiv · 1510.06219

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

A. Mielke·M. A. Peletier·D. R. M. Renger
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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.

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BibTeXRIS

A. Mielke, M. A. Peletier, D. R. M. Renger. 2015-10-21. A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility. https://doi.org/10.1515/jnet-2015-0073

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