Mode-coupling theory for aging in active glasses: relaxation dynamics and evolution towards steady state

Abstract

Aging refers to the evolution of system properties with waiting time $t_w$. It is a key feature of glassy dynamics. Recent experiments have demonstrated aging in biological systems that are inherently active with a magnitude of self-propulsion force $f_0$ and a persistence time $\ddot{I}{„}_p$. Thus, what governs the aging dynamics in these active systems has fundamental importance. We formulate a generic mode-coupling theory (MCT) of active glasses to address this question. The aging solutions of the theory show that the two-point correlation function decays more slowly with growing $t_w$, and the relaxation time $t_r$ increases. The activity-modification of the MCT critical point, $\hat{I}{»}_{\text{C}}$, has profound significance for active aging: the quench distance from $\hat{I}{»}_{\text{C}}$ governs aging and determines $\hat{I}´$, where $t_r\sim t_w^{\hat{I}}´$. $\hat{I}´$ decreases with increasing $f_0$, in agreement with existing simulations. However, the variation with $\ddot{I}{„}_p$ depends on the nature of activity. Our work has fundamental theoretical implications for active glasses and paves the way for a deeper understanding of the aging dynamics in biological systems.