Interacting particles in an activity landscape

We study interacting active Brownian particles (ABPs) with a space-dependent swim velocity via simulation and theory. We find that, although an equation of state exists, a mechanical equilibrium does not apply to ABPs in activity landscapes. The pressure difference originates in the flux of polar order and the gradient of swim velocity across the interface between regions of different activity. In contrast to motility-induced phase separation of ABPs with a homogeneous swim velocity, a critical point does not exist for an active-passive patch system, which continuously splits into a dense and a dilute phase with increasing activity. However, if the global density is so high that not all particles can be packed onto the inactive patch, then MIPS-like behavior is restored and the pressure is balanced again.