Correlation Functions as Hydrodynamic Green's Functions

Abstract

A formal solution for the thermodynamic variables describing a system in a nonequilibrium state is given in terms of space- and time-dependent correlation functions. The solution during the hydrodynamic stage is also given by the Green's function solution to the hydrodynamic equations. The correlation functions contain information, not contained in the Green's functions, about the initial relaxation of the system to the hydrodynamic stage. Comparison of the two solutions shows that the correlation functions are the propagators for the physically specified initial data, while the Green's functions are the propagators for a different set of initial data. General connective equations are obtained for the two sets of data by comparing the Green's function solution to the correlation function solution. Initial conditions for the hydrodynamic equations are not, in general, equal to the physical initial conditions because of the short initial "ageing" period during which the differential equations do not apply.