Past lectures

Abstract

We first introduce the basic setup of the hydrodynamical limits for stochastic systems. We then review the basic entropy methods and the logarithmic Soblev inequalities. As an application outside hydrodynamical limits, we shall derive the leading order estimate for the ground state energy of interacting Bosons. The relative entropy method will be proved in details and its application to the derivation of the Euler equations will be sketched. Finally we extend the relative entropy method to derive the Euler equations from quantum dynamics.