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 f₀ and a persistence time τ_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 in the regime when activity is not too large. 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, λ_C, has profound significance for active aging: the quench distance from λ_C governs aging and determines the aging exponent, δ, where t_r ∼ tδw. δ decreases with increasing f₀, in agreement with existing simulations. However, the variation with τ_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.