Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.

中文翻译：

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活性布朗球的相图：结晶和运动诱导相分离的亚稳定性。

运动诱导相分离（MIPS）是一种最简单且研究最广泛的非平衡相变示例，其中纯排斥活性颗粒经历了液相-气相分离。在这里，我们表明，MIPS共存状态实际上仅在非常宽泛的条件范围内对三维活性布朗粒子具有亚稳态，并通过有序过渡（我们称为活性结晶）长时间衰减。在刚好高于MIPS临界点的活动下，液-气双曲线被晶体-流体共存曲线所取代，固体，液体和气体都在两条曲线相交的三点处共存。然而，从无序的流体中形成活性晶体需要极少的波动，该波动表现出几乎密堆积的固相密度。仅在高活性下，并且仅在接近最大堆积的流体密度下，才可以在可行的时间尺度上克服相应的结晶障碍。这种平衡状态下的稠密液体所期望的玻璃态性会通过作用力大大降低，因此液-气共存的寿命会随着活性的增加而稳定下降，在模拟中表现为在极高的活性下易于自发结晶。