Motility-Induced Temperature Difference in Coexisting Phases

Unlike in thermodynamic equilibrium where coexisting phases always have the same temperature, here we show that systems comprising active self-propelled particles can self-organize into two coexisting phases at different kinetic temperatures, which are separated from each other by a sharp and persistent temperature gradient. Contrasting previous studies that have focused on overdamped descriptions of active particles, we show that a hot-cold coexistence occurs if and only if accounting for inertia, which is significant, e.g., in activated dusty plasmas, microflyers, whirling fruits, or beetles at interfaces. Our results exemplify a route to use active particles to create a self-sustained temperature gradient across coexisting phases. This phenomenon is fundamentally beyond equilibrium physics and is accompanied by a slow coarsening law with an exponent significantly smaller than the universal 1/3 exponent seen in both equilibrium systems and overdamped active Brownian particles.