  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 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 showing 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 which 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.
