Theory of Nonequilibrium Symmetry-Breaking Coexistence and Active Crystallization

Crystallization is perhaps the most familiar example of a symmetry-breaking transition. In equilibrium, thermodynamic arguments result in a powerful and convenient set of criteria for determining the coexistence curves associated with these transitions. In recent years, nonequilibrium symmetry-breaking transitions have been routinely observed in a variety of natural and synthetic systems. The breaking of detailed balance, and the resulting absence of Boltzmann statistics, motivates the need for a symmetry-breaking coexistence theory that is independent of the underlying distribution of microstates. Here, we develop such a theory, relying only on mechanics, balance laws, and system symmetries. In doing so, we develop a generalized Gibbs-Duhem relation that results in nonequilibrium coexistence criteria solely in terms of bulk equations of state. We apply our framework to active crystallization, developing a complete description of the phase diagram of active Brownian hard spheres. Our predicted phase diagram quantitatively recapitulates the solid-fluid coexistence curve as well as other key features of active phase behavior, such as the liquid-gas coexistence binodal and solid-liquid-gas triple point. It is our hope that our findings offer a concrete path forward towards the development of a general theory for nonequilibrium coexistence.