Large deviations and gradient flows

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

Research output: Contribution to journalArticleAcademicpeer-review

43 Citations (Scopus)


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. Keywords: large-deviation theory, non-equilibrium system, Wasserstein gradient flow
Original languageEnglish
Article number20120341
Pages (from-to)20120341-1/17
Number of pages17
JournalPhilosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences
Issue number2005
Publication statusPublished - 2013


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