Theory for the anomalous phase behavior of inertial active Brownian particles

In contrast to equilibrium systems, inertia can profoundly impact the phase behavior of active systems. This has been made particularly evident in recent years, with motility-induced phase separation (MIPS) exhibiting several intriguing dependencies on translational inertia. Here, we report extensive simulations characterizing the phase behavior of inertial active Brownian particles and develop a mechanical theory for the complete phase diagram without appealing to equilibrium notions. Our theory qualitatively captures all aspects of liquid-gas coexistence, including the critical value of inertia above which MIPS ceases. Notably, our findings highlight that particle softness, and not inertia, is responsible for the MIPS reentrance effect at the center of a proposed active refrigeration cycle.