  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).
