  As a result of the competition between self-propulsion and excluded volume
interactions, purely repulsive self-propelled spherical particles undergo a
motility-induced phase separation (MIPS). We carry out a systematic
computational study, considering several interaction potentials, systems
confined by hard walls or with periodic boundary conditions, and different
initial protocols. This approach allows us to identify that, despite its
non-equilibrium nature, the equations of state of Active Brownian Particles
(ABP) across MIPS verify the characteristic properties of first-order
liquid-gas phase transitions, meaning, equality of pressure of the coexisting
phases once a nucleation barrier has been overcome and, in the opposite case,
hysteresis around the transition as long as the system remains in the
metastable region. Our results show that the equations of state of ABPs
quantitatively account for their phase behaviour, providing a firm basis to
describe MIPS as an equilibrium-like phase transition.
