Entropic aging and extreme value statistics

TL;DR

This paper links entropic aging in glassy systems to extreme value statistics, showing that the long-term energy distribution follows standard extreme value distributions, and explores related physical systems.

Contribution

It establishes a precise connection between the Barrat-Mézard model's aging dynamics and extreme value theory, revealing the asymptotic energy distribution forms.

Findings

Long-time energy distribution follows Gumbel, Weibull, or Fréchet distributions.

Mapping provides exact asymptotic shape of energy distribution.

Highlights similarities with dissipative systems like granular gases.

Abstract

Entropic aging consists in a progressive slowing down of the low-temperature dynamics of a glassy system due to the rarefaction of downwards directions on the energy landscape, as lower and lower energy levels are reached. A prototypical model exhibiting this scenario is the Barrat-M\'ezard model. We argue that in the zero-temperature limit, this model precisely corresponds to a dynamical realization of extreme value statistics, providing an interesting connection between the two fields. This mapping directly yields the long-time asymptotic shape of the dynamical energy distribution, which is then one of the standard extreme value distributions (Gumbel, Weibull or Fr\'echet), thus restricting the class of asymptotic energy distributions with respect to the original preasymptotic results. We also briefly discuss similarities and differences between the Barrat-M\'ezard model and undriven dissipative systems like granular gases.