Multicomponent phase separation is a routine occurrence in both living and synthetic systems. Thermodynamics provides a straightforward path to determine the phase boundaries that characterize these transitions for systems at equilibrium. The prevalence of phase separation in complex systems outside the confines of equilibrium motivates the need for a nonequilibrium theory of multicomponent phase coexistence. Here, we develop a mechanical theory for coexistence that casts coexistence criteria into the familiar form of equality of state functions. Our theory generalizes traditional equilibrium notions such as the species chemical potential and thermodynamic pressure to systems out of equilibrium. Crucially, while these notions may not be identifiable for all nonequilibrium systems, we numerically verify their existence for a variety of systems by introducing the phenomenological multicomponent active model $\mathrm{B}+$. Our work establishes an initial framework for understanding multicomponent coexistence that we hope can serve as the basis for a comprehensive theory for high-dimensional nonequilibrium phase transitions.

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• Phase behavior
• Living matter & active matter
• Theories of collective dynamics & active matter