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arXiv · 1201.4601

Large deviations and gradient flows

Stefan Adams·Nicolas Dirr·Mark A. Peletier·Johannes Zimmer
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Abstract

In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on 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 generalises 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.

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Stefan Adams, Nicolas Dirr, Mark A. Peletier, Johannes Zimmer. 2012-01-22. Large deviations and gradient flows. https://doi.org/10.1098/rsta.2012.0341

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