Large deviations and gradient flows

S. Adams, N. Dirr, M. Peletier, J Zimmer

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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.
Original languageEnglish
Article number0341
JournalPhilosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
Issue number2005
Early online date18 Nov 2013
Publication statusPublished - 28 Dec 2013


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