  Classical nucleation theory (CNT), linking rare nucleation events to the free
energy landscape of a growing nucleus, is central to understanding phase-change
kinetics in passive fluids. Nucleation in non-equilibrium systems is much
harder to describe because there is no free energy, but instead a
dynamics-dependent quasi-potential that typically must be found numerically.
Here we extend CNT to a class of active phase separating systems governed by a
minimal field-theoretic model (Active Model B+). In the small noise and
supersaturation limits that CNT assumes, we compute analytically the
quasi-potential, and hence nucleation barrier, for liquid-vapor phase
separation. Crucially to our results, detailed balance, although broken
microscopically by activity, is restored along the instanton trajectory, which
in CNT involves the nuclear radius as the sole reaction coordinate.
