FLUCTUATION-DISSIPATION THEOREMS AND ENTROPY PRODUCTION IN RELAXATIONAL SYSTEMS

We show that for stochastic dynamical systems out of equilibrium the v iolation of the fluctuation dissipation equality is bounded by a funct ion of the entropy production. The result applies to a much wider situ ation than ''near equilibrium,'' comprising diffusion as well as glass es and other macroscopic systems far from equilibrium. For aging syste ms this bounds the age-frequency regimes in which the susceptibilities satisfy the fluctuation-dissipation theorem in terms of the rate of d ecay of the H function, a question intimately related to the reading o f a thermometer placed in contact with the system.