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Large deviations and gradient flows. (English) Zbl 1292.82023
Summary: 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.

MSC:
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
35R60 PDEs with randomness, stochastic partial differential equations
60F10 Large deviations
35K55 Nonlinear parabolic equations
60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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