Arrhenius-Type Description and Noise-Composition Dependence of Single-Vacancy Hopping in Active Brownian Crystals

We study vacancy-mediated hopping in a two-dimensional active Brownian-particle crystal with a single vacancy. Under active driving, the hopping rates are not organized by the free-particle effective noise amplitude alone. In contrast, in the passive limit, the hopping rate follows an Arrhenius-like activated trend with respect to the translational diffusion coefficient. Effective-noise comparisons show systematic dependence on the active fraction, indicating that the composition of thermal and persistent active fluctuations affects the hopping kinetics. These results demonstrate a breakdown of an effective-temperature description for microscopic defect-mediated transport in an active crystal.