  Nonequilibrium phase transitions are routinely observed in both natural and
synthetic systems. The ubiquity of these transitions highlights the conspicuous
absence of a general theory of phase coexistence that is broadly applicable to
both nonequilibrium and equilibrium systems. Here, we present a general
mechanical theory for phase separation rooted in ideas explored nearly a
half-century ago in the study of inhomogeneous fluids. The core idea is that
the mechanical forces within the interface separating two coexisting phases
uniquely determine coexistence criteria, regardless of whether a system is in
equilibrium or not. We demonstrate the power and utility of this theory by
applying it to active Brownian particles, predicting a quantitative phase
diagram for motility-induced phase separation in both two and three dimensions.
This formulation additionally allows for the prediction of novel interfacial
phenomena, such as an increasing interface width while moving deeper into the
two-phase region, a uniquely nonequilibrium effect confirmed by computer
simulations. The self-consistent determination of bulk phase behavior and
interfacial phenomena offered by this mechanical perspective provide a concrete
path forward towards a general theory for nonequilibrium phase transitions.
