  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 matter 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.
