Thermodynamics and statistical mechanics of frozen systems in inherent states

TL;DR

This paper applies a statistical mechanics framework to inherent states in glassy and granular systems, demonstrating that their distributions follow a generalized Gibbs measure and validating this with Monte Carlo simulations.

Contribution

It introduces a generalized Gibbs measure for inherent states in non-thermal systems and validates it through Monte Carlo simulations of lattice models.

Findings

Inherent states follow a generalized Gibbs distribution.

Monte Carlo simulations show agreement between time averages and distribution predictions.

The approach is applicable to non-thermal systems like granular materials.

Abstract

We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular we consider three lattice models (a diluted Spin Glass, a monodisperse hard-sphere system under gravity and a hard-sphere binary mixture under gravity) undergoing a schematic ``tap dynamics'', showing via Monte Carlo calculations that the time average of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to non thermal systems.