We calculate the bulk-diffusion coefficient and the conductivity in nonequilibrium conserved-mass aggregation processes on a ring. These processes involve chipping and fragmentation of masses, which diffuse on a lattice and aggregate with their neighboring masses on contact, and, under certain conditions, they exhibit a condensation transition. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility of masses, is greatly enhanced. The enhancement in the conductivity, in accordance with the Einstein relation, results in large mass fluctuations and can induce a mobility-driven clustering in the systems. Indeed, in a certain parameter regime, we show that the conductivity, along with the mass fluctuation, diverges beyond a critical density, thus characterizing the previously observed nonequilibrium condensation transition [Phys. Rev. Lett. 81, 3691 (1998)] in terms of an instability in the conductivity. Notably, the bulk-diffusion coefficient remains finite in all cases. We find our analytic results in quite good agreement with simulations.

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大规模聚集过程中的运输和波动：移动性驱动的集群

我们计算了环上非平衡保守质量聚集过程中的体扩散系数和电导率。这些过程涉及物质的碎裂和破碎，这些物质在晶格中扩散并在接触时与其相邻的物质聚集，并且在某些条件下，它们表现出缩合转变。我们发现，即使在没有微观时间可逆性的情况下，该系统也满足爱因斯坦关系，该关系将电导率与体积扩散系数之比与质量波动联系起来。有趣的是，当聚集作用占主导地位时，电导率或等价物的迁移率将大大提高。根据爱因斯坦关系式，电导率的提高，会导致较大的质量波动，并可能导致系统中由移动性驱动的群集。实际上，在一定的参数范围内，我们显示出电导率以及质量波动超出了临界密度，从而表征了先前观察到的非平衡缩合转变[物理 莱特牧师 81，3691（1998）]在导电性的不稳定性方面。值得注意的是，在所有情况下，体扩散系数都保持有限。我们发现分析结果与模拟结果非常吻合。