Wasserstein gradient flows from large deviations of thermodynamic limits

2012/03/03 by Duong, Manh Hong, Laschos, Vaios, Renger, Michiel
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1203.0676

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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