Quasi-equilibrium in glassy dynamics: an algebraic view

TL;DR

This paper introduces a formalism linking slow glassy dynamics to equilibrium states, showing that under certain conditions, long-time relaxational behavior can be understood as quasi-equilibrium in mean field models.

Contribution

It presents a novel algebraic approach to describe glassy dynamics as a quasi-equilibrium process, connecting constrained equilibrium chains to real relaxational dynamics in mean field models.

Findings

Long-time dynamics can be described by a constrained equilibrium formalism.

In mean field spin glasses, Langevin dynamics equations are recovered at the dynamical transition.

The approach offers a new perspective on slow dynamics and enables computation of new dynamical quantities.

Abstract

We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of long chain where each bond is close to the previous one. We show that in specific conditions this pseudo-dynamic process can formally describe real relaxational dynamics the long time. In particular, in mean field spin glass models we can recover in this way the equations of Langevin dynamics in the long time limit at the dynamical transition temperature and below. We interpret the formal identity as an evidence that in these situations the configuration space is explored in a quasi-equilibrium fashion. Our general formalism, that relates dynamics to equilibrium puts slow dynamics in a new perspective and opens the way to the computation of new dynamical quantities in glassy systems.