Entropic and gradient flow formulations of nonlinear diffusion

We consider nonlinear diffusion equations that arise as scaling limit of certain interacting particle systems, the zero range process. We show that they are the gradient flow of the thermodynamic entropy of the process with respect to a weighted Wasserstein metric, where the weight is related to the diffusion of a tagged particle.

(Joint work with Mark Peletier, Marios Stamatakis and Johannes Zimmer)