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As a result of the competition between self-propulsion and excluded volumeinteractions, purely repulsive self-propelled spherical particles undergo amotility-induced phase separation (MIPS). We carry out a systematiccomputational study, considering several interaction potentials, systemsconfined by hard walls or with periodic boundary conditions, and differentinitial protocols. This approach allows us to identify that, despite itsnon-equilibrium nature, the equations of state of Active Brownian Particles(ABP) across MIPS verify the characteristic properties of first-orderliquid-gas phase transitions, meaning, equality of pressure of the coexistingphases once a nucleation barrier has been overcome and, in the opposite case,hysteresis around the transition as long as the system remains in themetastable region. Our results show that the equations of state of ABPsquantitatively account for their phase behaviour, providing a firm basis todescribe MIPS as an equilibrium-like phase transition.

Active Brownian Equation of State: Metastability and Phase Coexistence