Wasserstein gradient flows from large deviations of thermodynamic limits
  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. 
Manh Hong Duong, Vaios Laschos, Michiel Renger
math.AP math-ph math.MP math.OC