Local quasi-equilibrium description of slow relaxation systems.

We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is derived, and from it we obtain the relaxation equation for the moments. We show that the fluctuation-dissipation theorem can be formulated in terms of the temperature of the system at local quasi-equilibrium which is related to that of the bath by means of a scaling factor revealing lack of thermal equilibrium. Our theory may be applied to a wide variety of systems undergoing slow relaxation. We discuss in particular slow dynamics in glassy systems and Brownian motion in a granular gas.