Cooling Mechanism Controls Motility-Induced Phase Separation in Inertial Active Liquids

Motility-induced phase separation (MIPS) is a central collective phenomenon in active matter, theoretically established in the overdamped regime. We discover that the dynamical origin of MIPS is fundamentally altered by inertia, which induces a cooling mechanism absent in overdamped active matter. This conclusion is supported by an active variant of the direct simulation Monte Carlo method and by a kinetic theory for inertial self-propelled hard spheres derived from the microscopic dynamics. In contrast to the overdamped case, both analyses demonstrate that inertial MIPS can occur even without impenetrability, as it originates from a density-dependent cooling mechanism due to the coupling of density, orientation, and temperature. This mechanism emerges from the competition between activity and a density-dependent collision rate arising from spatial correlations between colliding particles. These findings open a pathway to fundamentally connect inertial active matter with granular physics.