Fluctuation-Dissipation theorems and entropy production in relaxational systems

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Abstract
We show that for stochastic dynamical systems out of equilibrium the violation of the fluctuation-dissipation equality is bounded by a quantity proportional to the square root of the entropy production. The result applies to a much wider situation than the `near equilibrium' regime usually discussed in non-equilibrium thermodynamics, comprising diffusion as well as glasses and other macroscopic systems far from equilibrium. For aging systems this gives bounds in terms of the asymptotic rate of decay of the H-function on the age-frequency regimes in which the susceptibilities satisfy FDT, a question intimately related to the reading of a thermometer placed in contact with the system.

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