Entropy properties of nonlocal diffusion equations

Nonlocal diffusion equations are evolution equations which resemble the heat equation except that, instead of describing an ensemble of a large number of particles undergoing Brownian motion, the particles are instead governed by a jump process. In this talk, I will explain a variational perspective on nonlocal equations, which is suggested by optimal transport as well as the second law of thermodynamics. Time permitting, I will outline possible future applications to sampling algorithms for non-log-Sobolev distributions.