Relative entropy and hydrodynamics of Ginzburg-Landau models

We prove the hydrodynamic limit of Ginzburg-Landau models by considering relative entropy and its rate of change with respect to local Gibbs states. This provides a new understanding of the role played by relative entropy in the hydrodynamics of interacting particle systems.Work partially supported by U.S. National Science Foundation Grant. DMS-8806731 and Army Grant ARO-DAAL 03-88-K-0047.