Abstract
Stationary ensemble averages such as < X n >, < XY > etc. where X and Y are stochastic variables whose changes in the course of time t are additive, are examined for a system with dynamics described by a master equation. Results are obtained for the two important cases of ( a ) thermal equilibrium and ( b ) steady-state situations brought about by the imposition of external fields. The averages are expressed as integrals with respect to time of appropriate time-correlation functions. For appropriate quantities of this type one may express corresponding linear response coefficients in terms of these averages. The results represent many-body generalizations of the elementary Einstein relations between diffusion coefficient and mean-square displacement, and between mobility and mean-square displacement. While the former type of relation holds only for normal diffusive systems the second type holds also for anomalous diffusive systems.
Published Version
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