Large deviations and gradient flows

Adams, Steffan, Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367, Peletier, Mark and Zimmer, Johannes 2013. Large deviations and gradient flows. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371 (2005) , 20120341. 10.1098/rsta.2012.0341

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Abstract

In recent work we uncovered intriguing connections between Otto’s characterization of diffusion as an entropic gradient flow on the 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 generalizes 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	The Royal Society
ISSN:	1364-503X
Last Modified:	27 Oct 2022 09:41
URI:	https://orca.cardiff.ac.uk/id/eprint/67303

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