Statistics of Thermal Avalanches in Driven Amorphous Systems

TL;DR

This paper models the statistics of thermal avalanches in driven amorphous systems near instability, revealing nonPoisson waiting times, aging dynamics, and detailed distributions of avalanche sizes and counts.

Contribution

It introduces a generalized Master equation framework that captures nonMarkovian aging dynamics and provides full counting statistics for avalanche behaviors.

Findings

NonPoisson waiting time statistics due to stringy excitations

NonMarkovian aging dynamics in avalanche clusters

Complete distributions of avalanche magnitudes and counts

Abstract

Within the framework of the random first-order transition theory of glasses, we discuss the statistics of thermal avalanches, the large scale rearrangements in driven amorphous systems near their instability. Stringy excitations yield nonPoisson waiting time statistics. Embedding these statistics in a generalized Master equation captures the nonMarkovian, aging dynamics of avalanche clusters. We apply this framework to analyze nonequilibrium signatures of thermal avalanches, auto correlation functions and effective temperatures, under both quasi static shear and stochastic shaking protocols. We use full counting statistics to derive the complete distribution of both the avalanche magnitudes and avalanche counts, uncovering the intermediate time behavior.