A dissipation of relative entropy by diffusion flows

Abstract

Given a probability measure, we consider the diffusion flows of probability measures associated with the partial differential equation (PDE) of Fokker-Planck. Our flows of the probability measures are defined as the solution of the Fokker-Planck equation for the same strictly convex potential, which means that the flows have the same equilibrium. Then, we shall investigate the time derivative for the relative entropy in the case where the object and the reference measures are moving according to the above diffusion flows, from which we can obtain a certain dissipation formula and also an integral representation of the relative entropy.