A scenario for the dynamics in the small intropy production limit

We present a scenario for the nonequilibrium dynamics in the limit of small entropy production. We discuss (i) the appearence of different time-scales, (ii) the modification of the fluctuation-dissipation theorem and its relation to effective temperatures and partial equilibrations and (iii) the validity of Onsager reciprocity relations. We distinguish these properties by their reaction to infinitesimal perturbations. We recall that one can easily change the time dependence of observables by applying an infinitesimal force while time-reparametrization invariant features remain unchanged under the same perturbations. With the aim of better understanding these properties, we consider the effect of several baths with different temperatures and time-scales on the dynamics. This is done in two ways: numerically, by using a especially developed Monte Carlo algorithm that mimics the coupling to multiple baths; analytically, by computing the time-dependent probability density of simple systems in contact with multiple baths. We finally argue that these features are related to supersymmetry, the reparametrization invariance of the slow dynamics and its spontaneous breaking. This scenario is consistent within any perturbative scheme. A brief version of this article appeared in Physica A263, 242 (1999).