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

Source: [Arrhenius-Type Description and Noise-Composition Dependence of Single-Vacancy Hopping in Active Brownian Crystals](<https://www.sota2.com/research/paper/6a55c26632fb93731487749e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-29T05:00:05.450Z

Authors: Hiroto Tomida, Yoshihiro Yamazaki

Published: 2026-07-11T08:07:03.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2607.10192>)

[PDF](<https://arxiv.org/pdf/2607.10192.pdf>)