  Non-aligning self-propelled particles with purely repulsive excluded volume
interactions undergo athermal motility-induced phase separation into a dilute
gas and a dense cluster phase. Here, we use enhanced sampling computational
methods and analytic theory to examine the kinetics of formation of the dense
phase. Despite the intrinsically nonequilibrium nature of the phase transition,
we show that the kinetics can be described using an approach analogous to
equilibrium classical nucleation theory, governed by an effective free energy
of cluster formation with identifiable bulk and surface terms. The theory
captures the location of the binodal, nucleation rates as a function of
supersaturation, and the cluster size distributions below the binodal, while
discrepancies in the metastable region reveal additional physics about the
early stages of active crystal formation. The success of the theory shows that
a framework similar to equilibrium thermodynamics can be obtained directly from
the microdynamics of an active system, and can be used to describe the kinetics
of evolution toward nonequilibrium steady states.
