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

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 $\tau_p$. 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, $\lambda_\text{C}$, has profound significance for active aging: the quench distance from $\lambda_\text{C}$ governs aging and determines $\delta$, where $t_r\sim t_w^\delta$. $\delta$ decreases with increasing $f_0$, in agreement with existing simulations. However, the variation with $\tau_p$ 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.