Logarithmic aging via instability cascades in disordered systems

TL;DR

This paper uncovers the structural mechanism behind logarithmic aging in disordered systems, showing how self-organized metastable states and aging avalanches cause slow, history-dependent relaxation.

Contribution

It introduces experimental and simulation evidence that aging results from the system approaching an instability threshold, leading to self-similar avalanches and logarithmic relaxation.

Findings

Aging involves metastable states near instability thresholds.

Relaxation occurs via self-similar avalanches with increasing dwell times.

Logarithmic aging is due to slow growth of energy barriers.

Abstract

Many complex and disordered systems fail to reach equilibrium after they have been quenched or perturbed. Instead, they sluggishly relax toward equilibrium at an ever-slowing, history-dependent rate, a process termed physical aging. The microscopic processes underlying the dynamic slow-down during aging and the reason for its similar occurrence in different systems remain poorly understood. Here, we reveal the structural mechanism underlying logarithmic aging in disordered mechanical systems, through experiments in crumpled sheets and simulations of a disordered network of bi-stable elastic elements. We show that under load, the system self-organizes to a metastable state poised on the verge of an instability, where it can remain for long, but finite times. The system's relaxation is intermittent, advancing via rapid sequences of instabilities, grouped into self-similar, aging avalanches. Crucially, the quiescent dwell times between avalanches grow in proportion to the system's age, due to a slow increase of the lowest effective energy barrier, which leads to logarithmic aging.