  Motility-induced phase separation (MIPS) is of great importance and has been
extensively researched in overdamped systems, nevertheless, what impacts
inertia will bring on kinetics of MIPS is lack of investigation. Here, we find
that, not only the phase transition changes from continuous to discontinuous,
but also the formation of clusters exhibits a nucleation-like process without
any coarsening regime, different from spinodal decomposition in the overdamped
case. This remarkable kinetics stems from a competition between
activity-induced accumulation of particles and inertia-induced suppression of
clustering process. More interestingly, the discontinuity of MIPS still exists
even when the ratio of particle mass to the friction coefficient reduces to be
very small such as 0.0001. Our findings emphasize the importance of inertia in
kinetics of MIPS, and may open a new perspective on understanding the nature of
MIPS in active systems.
