Motility-induced phase separation is reentrant

Active Brownian particles (ABPs) with pure repulsion is an ideal model to understand the effect of nonequilibrium on collective behaviors. It has long been established that activity can create effective attractions leading to motility-induced phase separation (MIPS), whose role is similar to that of (inverse) temperature in the simplest equilibrium system with attractive inter-particle interactions. Here, we report that activity can lead to a counterintuitive reentrant MIPS, which is completely different from the phase behavior of equilibrium systems, shown by both simulations and theory. Our theoretical analysis based on a kinetic theory of MIPS shows that an additional term of activity-induced nonequilibrium vaporization is able to hinder the formation of dense phase when activity is large enough. Such effect along with the activity-induced effective attraction thus lead to the MIPS reentrance. Numerical simulations verify this nonequilibrium effect induced solely by activity on phase behaviors of ABPs, and further demonstrate the dependence of MIPS on activity and the strength of inter-particle interaction predicted by our theoretical analysis. Our findings highlight the particular role played by the nonequilibrium nature of activity on phase behaviors of active systems, which may inspire deep insights into the essential difference between equilibrium and nonequilibrium systems.