# Non equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model

## TL;DR

This paper investigates the non-equilibrium dynamics of a classical disordered Hamiltonian p-spin model, revealing various long-term behaviors including equilibrium, metastability, and aging, depending on initial and final parameters.

## Contribution

It introduces a classical analog of quantum quenches in disordered systems and maps out a dynamic phase diagram with distinct equilibrium and out-of-equilibrium phases.

## Key findings

- System can equilibrate or remain out of equilibrium after a quench.
- Out-of-equilibrium states include metastable and aging regimes.
- Identifies a phase diagram with one equilibrium and two non-equilibrium phases.

## Abstract

We study the dynamics of a classical disordered macroscopic model completely isolated from the environment reproducing, in a classical setting, the "quantum quench" protocol. We show that, depending on the pre and post quench parameters the system approaches equilibrium, succeeding to act as a bath on itself, or remains out of equilibrium, in two different ways. In one of the latter, the system stays confined in a metastable state in which it undergoes stationary dynamics characterised by a single temperature. In the other, the system ages and its dynamics are characterised by two temperatures associated to observations made at short and long time differences (high and low frequencies). The parameter dependence of the asymptotic states is rationalised in terms of a dynamic phase diagram with one equilibrium and two out of equilibrium phases. Aspects of pre-thermalisation are observed and discussed. Similarities and differences with the dynamics of the dissipative model are also explained.