Active Hard Spheres in Infinitely Many Dimensions

Few equilibrium—even less so nonequilibrium—statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical equilibrium hard spheres in infinitely many space dimensions are a notable exception. We show here that dimensionality is a powerful organizing device for exploring collective properties of active hard spheres evolving far from equilibrium. In infinite dimensions, we exactly compute the stationary state properties that govern and characterize the collective behavior of active hard spheres: the structure factor, the equation of state for the pressure and the self-propulsion velocity. We show that this allows to account for motility-induced phase separation.