  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 robust feature, independent of
system size. 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.
