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arXiv · 1203.0676

Wasserstein gradient flows from large deviations of thermodynamic limits

Manh Hong Duong·Vaios Laschos·Michiel Renger
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Abstract

We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the rate functional, that characterizes the large deviations from the hydrodynamic limit, in a way that the free energy appears explicitly. Next we use this formulation via the contraction principle to prove that the discreet time rate functional is asymptotically equivalent in the Gamma-convergence sense to the functional derived from the Wasserstein gradient discretization scheme.

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Manh Hong Duong, Vaios Laschos, Michiel Renger. 2012-03-28. Wasserstein gradient flows from large deviations of thermodynamic limits. https://arxiv.org/abs/1203.0676

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