Large deviations and gradient flows

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

Research output: Contribution to journalArticle

21 Citations (Scopus)
120 Downloads (Pure)


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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