Mini-workshop: Particle systems with several conservation laws: fluctuations and hydrodynamic limit (Q2577101)

Summary: The Mini-Workshop is concerned with the large-scale description of microscopic many-particle systems with two or more conservation laws. This is a 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. Contributions: -- Angela Stevens (joint with Hyung Ju Hwang, Kyungkeun Kang, Frithjof Lutscher), Hyperbolic models for chemosensitive movement in interacting cell systems, p.~1203; -- Attila Rákos (joint with Gunter M. Schütz), Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities, p.~1204; -- Bernard Derrida, Exact steady state of exclusion processes with several species of particles, p.~1206; -- József Fritz (joint with Bálint Tóth), Hyperbolic systems: Hydrodynamic limits via PDE methods, p.~1207; -- Stefano Olla, Hydrodynamic limit for the Fourier's law, p. 1210; -- Benedek Valkso (joint with Bálint Tóth), Perturbation of equilibria: a hydrodynamic limit, p.~1213 -- Vladislav Popkov (joint with Gunter M. Schütz), Vanishing viscosity term in hydrodynamic description of multispecies driven particle systems with open boundaries, p.~1215;--Stefan Großkinsky, Equivalence of ensembles for two-component zero-range invariant measures, p.~1218\; -- Alan M. Hammond (joint with Fraydoun Rezakhanlou), The kinetic limit of a system of coagulating Brownian particles, p.~1220; -- Athanasios E. Tzavaras, Relative entropy in hyperbolic relaxation, p.~1224; -- Pierre-Emmanuel Jabin (joint with François James), Linear transport equations with fast scales, p.~1226.