Theory of Nonequilibrium Crystallization and the Phase Diagram of Active Brownian Hard Spheres

The crystallization of hard spheres at equilibrium is perhaps the most familiar example of an entropically-driven phase transition. In recent years, it has become clear that activity can dramatically alter this order-disorder transition in unexpected ways. The theoretical description of active crystallization has remained elusive as the traditional thermodynamic arguments that shape our understanding of passive freezing are inapplicable to active systems. Here, we develop a statistical mechanical description of the one-body density field and a nonconserved order parameter field that represents local crystalline order. We leverage our recent dynamical theory of coexistence to construct the full phase diagram of active Brownian spheres, quantitatively recapitulating the solid-fluid coexistence curve, the liquid-gas coexistence binodal, and solid-liquid-gas triple point. We develop equations of state describing the crystallinity field, suggesting that increasing activity decreases the preferred crystalline order for a fixed density and shifts the order-disorder transition to higher packing fractions.