Local quasi-equilibrium description of slow relaxation systems

TL;DR

This paper develops a dynamical framework for slow relaxation systems using an extension of Onsager's fluctuation theory, deriving a non-Markovian Fokker-Planck equation and connecting fluctuation-dissipation to local quasi-equilibrium temperature.

Contribution

It introduces a novel theoretical approach to describe slow relaxation processes via local quasi-equilibrium and non-Markovian dynamics, applicable to glassy systems and granular gases.

Findings

Derived a non-Markovian Fokker-Planck equation for slow systems.

Formulated fluctuation-dissipation theorem in terms of local quasi-equilibrium temperature.

Applicable to diverse slow relaxation phenomena in complex systems.

Abstract

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. 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.