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

TL;DR

This paper develops a mode-coupling theory to understand aging in active glasses, revealing how activity influences relaxation dynamics and the approach to steady state, with implications for biological systems.

Contribution

It introduces a generic MCT framework for active glasses, showing how activity modifies aging behavior and critical points, aligning with simulation results.

Findings

Aging correlation functions decay more slowly with increased waiting time.

Relaxation time scales as a power law with waiting time, t_r ~ t_w^δ.

Activity parameters f_0 and τ_p significantly influence aging dynamics.

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 $\tau_p$. 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.