Wasserstein gradient flows from large deviations of thermodynamic limits
Analysis of PDEs
2012-03-29 v2 Mathematical Physics
math.MP
Optimization and Control
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.
Cite
@article{arxiv.1203.0676,
title = {Wasserstein gradient flows from large deviations of thermodynamic limits},
author = {Manh Hong Duong and Vaios Laschos and Michiel Renger},
journal= {arXiv preprint arXiv:1203.0676},
year = {2012}
}