Time Correlations and Fluctuations

Abstract

We developed a simple picture of the macroscopic, large scale description of fluids: on a sufficiently coarse space-time scale the locally conserved fields are deterministic and are governed by the hydrodynamic equations. A very natural idea is to refine now the scale of observation such as to discern the fluctuating deviations from the deterministic law. We consider only the case of thermal equilibrium. The extension to local equilibrium states is then a small further step. We will explain the theory for the case of fluctuating hydrodynamics. But in fact the method to be developed is very general and in particular applicable to the various kinetic equations.