Kinetics of motility-induced phase separation and swim pressure

Active Brownian particles (ABPs) represent a minimal model of active matter consisting of self-propelled spheres with purely repulsive interactions and rotational noise. Here we examine the pressure of ABPs in two dimensions in both closed boxes and systems with periodic boundary conditions and show that its nonmonotonic behavior with density is a general property of ABPs and is not the result of finite-size effects. We correlate the time evolution of the mean pressure towards its steady-state value with the kinetics of motility-induced phase separation. For parameter values corresponding to phase-separated steady states, we identify two dynamical regimes. The pressure grows monotonically in time during the initial regime of rapid cluster formation, overshooting its steady-state value and then quickly relaxing to it, and remains constant during the subsequent slower period of cluster coalescence and coarsening. The overshoot is a distinctive feature of active systems.