title: Large deviations and gradient flows.
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.
authors.affiliation: Mathematics Institute, University of Warwick, , Coventry, UK.
authors.forename: Stefan
authors.initials: S
authors.lastname: Adams
authors.forename: Nicolas
authors.initials: N
authors.lastname: Dirr
authors.forename: Mark
authors.initials: M
authors.lastname: Peletier
authors.forename: Johannes
authors.initials: J
authors.lastname: Zimmer
keywords: Wasserstein gradient flow; large-deviation theory; non-equilibrium system