  Motility-induced phase separation (MIPS) arises generically in fluids of
self-propelled particles when interactions lead to a kinetic slowdown at high
densities. Starting from a continuum description of scalar active matter, akin
to a generalized Cahn-Hilliard equation, we give a general prescription for the
mean densities of coexisting phases in flux-free steady states that amounts, at
a hydrodynamics scale, to extremizing an effective free energy. We illustrate
our approach on two well-known models: self-propelled particles interacting
either through a density-dependent propulsion speed or via direct pairwise
forces. Our theory accounts quantitatively for their phase diagrams, providing
a unified description of MIPS.
