Predicting the phase behavior of mixtures of active spherical particles

An important question in the field of active matter is whether or not it is possible to predict the phase behavior of these systems. Here, we study the phase coexistence of binary mixtures of torque-free active Brownian particles for both systems with purely repulsive interactions and systems with attractions. Using Brownian dynamics simulations, we show that phase coexistences can be predicted quantitatively for these systems by measuring the pressure and "reservoir densities." Specifically, in agreement with the previous literature, we find that the coexisting phases are in mechanical equilibrium, i.e., the two phases have the same pressure. Importantly, we also demonstrate that the coexisting phases are in chemical equilibrium by bringing each phase into contact with particle reservoirs and show that for each species, these reservoirs are characterized by the same density for both phases. Using this requirement of mechanical and chemical equilibrium, we accurately construct the phase boundaries from properties that can be measured purely from the individual coexisting phases. This result highlights that torque-free active Brownian systems follow simple coexistence rules, thus shedding new light on their thermodynamics.