# The dissipation theorem

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Late in 2006 we derived a new and very widely applicable theorem for nonequilibrium statistical mechanics. This theorem shows that the argument of the Evans-Searles FT is also central to nonlinear response theory. The ensemble averaged response of an arbitrary phase function is related to the time integral of the transient time correlation function formed by ensemble averaging the product of the dissipation function evaluated at time zero (the initial state) and the phase function being studied, as a function of time. This expression for the time dependent response is exact arbitrarily far from equilibrium. It applies to all types of nonequilibrium systems including those for which there is an explicit external field driving the system away from equilibrium, and it is also the case where the nonequilibrium state is generated by an initial distribution that is not preserved by the dynamics. The theorem shows that the dissipation function is the central function for nonequilibrium statistical mechanics. The close to equilibrium dissipation theorem reduces to the well-known expressions of linear response theory.