Wasserstein gradient flows from large deviations of thermodynamic limits

Details Wasserstein gradient flows from large deviations of thermodynamic limits Wasserstein gradient flows from large deviations of thermodynamic limits

2012-03-03

arxiv.org/abs/1203.0676v2

Mathematics

Analysis of PDEs

Scientific paper

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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