Translational and rotational temperature difference in coexisting phases of inertial active dumbbells

We investigate the effect of translational and rotational inertia on motility-induced phase separation in underdamped active dumbbells and identify the emergence of four distinct kinetic temperatures across the coexisting phases-unlike in overdamped systems. We find that the dilute, gas-like phase consistently exhibits a higher translational kinetic temperature than the dense, liquid-like phase, with this difference amplified by increasing the rotational inertia. Rotational kinetic temperatures display a similar trend, with the dense phase remaining colder than the dilute phase; however, in this case, the temperature difference grows with translational inertia and activity while becoming practically independent of rotational inertia. This counterintuitive behavior arises from the interplay of activity-driven collisions with both translational and rotational inertia in the coexisting phases. Our results highlight the critical role of translational and rotational inertia in shaping the kinetic temperature landscape of motility-induced phase separation and offer new insights into the nonequilibrium thermodynamics of active matter.