Mini-Workshop: Particle Systems with Several Conservation Laws: Fluctuations and Hydrodynamic Limit

Abstract

The Mini-Workshop is concerned with the large-scale description of microscopic many-particle systems with two or more conservation laws. This is topic of common interest for statistical mechanics, probability theory and PDE theory. The main difficulty lies in the proof of the hydrodynamic limit in terms of a system of (generically hyperbolic) PDE’s which includes a proper treatment of shock and boundary discontinuities that result from the microscopic dynamics. Moreover, fundamental properties of current-carrying stationary states of such systems (which are not Gibbs states) are studied in terms of fluctuations of macroscopic quantities. Many powerful tools developed for particle systems (or PDE’s respectively) with one conservation law have no obvious generalization to systems with two or more conservation laws and hence new mathematical ideas need to be developed.