Workshop on Macroscopic Modeling of Materials with Fine Structure

Carnegie Mellon University, Pittsburgh, PA
May 26–28, 2011

Abstract: Since a famous article by Jordan, Otto and Kinderlehrer, it is well-known that the Fökker-Planck equation can be described as a gradient flow of free energy in the Wasserstein metric. It is common in gradient flow structures that the metric can be interpreted as the dissipation or energy loss of the system. However, it is not immediately clear how the Wasserstein metric can be viewed as such. To understand this, we switch to a particle system that can be interpreted as a microscopic model for the continuum equation. It turns out that the Wasserstein gradient flow is closely related to the large-deviation behaviour of such systems.

Center for Nonlinear Analysis | Department of Mathematical Sciences | Carnegie Mellon