The Mechanical Theory of Active Crystallization

The equilibrium crystallization transition of hard spheres is among the most familiar examples of an entropically-driven order-disorder phase transition. Recently, it has been shown that crystallization can also be driven by activity in models of active Brownian hard spheres. The breaking of detailed balance, and the resulting absence of Boltzmann statistics, motivates the development of a theory of symmetry-breaking transitions that is independent of the underlying distribution of microstates. Here, we develop such a theory, leveraging mechanics, conservation laws, and symmetries to describe crystal-fluid coexistence in both equilibrium and nonequilibrium systems. We apply our framework to active crystallization, deriving the coexistence criteria for active crystal-fluid coexistence in terms of bulk equations of state. We perform particle-based simulations to obtain these equations of state, allowing for a complete description of the phase diagram of active Brownian hard spheres. Our predicted phase diagram quantitatively recapitulates the crystal-fluid coexistence curve as well as other key features of active phase behavior, including the triple point. Our findings offer a concrete path forward towards the development of a general theory for coexistence when both conserved and nonconserved order parameters are coupled.