Hydrodynamics and Beyond : Deterministic and fluctuating behavior in macroscopic systems.
Joel Lebowitz (IHES, Rutgers)

Jeudi 10 avril 1997

Starting with an overview of equilibrium I will review some recent developments in the rigorous derivation of hydrodynamic-type macroscopic equations from a simple microscopic models.

The deterministic evolution of hydrodynamic variables emerges as the "law of large numbers", which holds with probability one in the limit in which the ratio of the microscopic to the macroscopic spatial and temporal scales go to zero. There are corrections to this evolution, both deterministic and random, for real systems where the micro/macro ratio is small but non zero.

These can become very important in cases where the solution of the hydrodynamic equation is unstable and/or one considers long macroscopic times.