Statistics of thermal avalanches in driven amorphous systems

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 non-Poisson waiting-time statistics. Embedding these statistics in a generalized master equation captures the non-Markovian, 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.