Escape dynamics of active Brownian particles with multimodal diffusion

Abstract

Escape dynamics of active particles plays a critical role in understanding biochemical reactions. Previous experiments have revealed multimodal protein diffusion in live Escherichia coli, with a distribution of diffusion modes peaked in the subdiffusive regime. However, the influence of such multimodal diffusion on active transport dynamics remains unclear. To address this, we analyze the escape rates of active Brownian particles in a double-well potential by comparing particles with multiple diffusion modes to those with a single mode. For particles exhibiting a single diffusion mode, escape rates increase significantly in subdiffusive regimes as the active noise strength grows, while superdiffusive regimes show slight variations. This occurs because subdiffusive particles are more likely to be trapped in the potential well, which thereby reduces the probability of barrier crossing. Building on these results, we find that multiple diffusion modes can modulate average escape rates of active Brownian particles. For distributions centered on normal or superdiffusive modes, the average escape rate increases with the probability weight of the central mode. In contrast, when the central tendency of the diffusion-mode distribution lies in the subdiffusive regime, the average escape rate exhibits bidirectional behavior, either increasing or decreasing, which depends on the relative weights of diffusion modes. Furthermore, a comparative analysis of Gaussian diffusion-mode distributions against Laplace, Cauchy, and experimentally derived distributions reveals that heavy-tailed characteristics in the superdiffusive regime can enhance average escape rates beyond those predicted by the Gaussian distribution.