Passive memory reshapes active persistence
Many active systems move in complex environments whose mechanical response is slow and history dependent. To address this regime, we study the collective dynamics of self-sustained active particles in non-Markovian media within a generalized Langevin framework with memory. We focus on the competition between the timescales of active persistence and viscoelastic relaxation in the environment. Using a minimal interacting model with an exponential memory kernel, we show that environmental memory qualitatively reshapes motility-induced phase separation of self-propelled active particles. When the memory timescale is comparable to the active persistence time, delayed response generates an effective anti-persistence that suppresses clustering and produces a broad metastable regime with slow nucleation dynamics. By contrast, for long memory timescales, reduced friction at short times enhances the effective propulsion velocity and restores phase separation. Our results demonstrate that the surrounding medium can actively regulate the emergence, stability, and dynamics of collective organization in active matter.