Large deviations and gradient flows
Abstract
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. In this paper, we sketch this connection, show how it generalises to a wider class of systems, and comment on consequences and implications. Specifically, we connect macroscopic gradient flows with large deviation principles, and point out the potential of a bigger picture emerging: we indicate that in some non- equilibrium situations, entropies and thermodynamic free energies can be derived via large deviation principles. The approach advocated here is different from the established hydrodynamic limit passage but extends a link that is well known in the equilibrium situation.
Cite
@article{arxiv.1201.4601,
title = {Large deviations and gradient flows},
author = {Stefan Adams and Nicolas Dirr and Mark A. Peletier and Johannes Zimmer},
journal= {arXiv preprint arXiv:1201.4601},
year = {2014}
}