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The Gallavotti-Cohen fluctuation theorem suggests a general symmetry in the fluctuations of the entropy production, a basic concept in the theory of irreversible processes, based on results in the theory of strongly chaotic maps. We study this symmetry for some standard models of nonequilibrium steady states. We give a general strategy to derive a local fluctuation theorem exploiting the Gibbsian features of the stationary space-time distribution. This is applied to spin flip processes and to the asymmetric exclusion process. Dedicated in honor of Robert Minlos on the occasion of his 70th birthday.

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