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Large deviations and gradient flows

Adams, Steffan, Dirr, Nicolas P., 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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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: 20 Dec 2017 03:02

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