活性布朗粒子的上坡与下坡首次通过：不对称性与精确路径重加权

中文摘要 AI 辅助

活性系统中的首次通过过程将随机输运与自推进和取向持久性相结合，使得沿外部偏置和逆外部偏置的运动对内部活性动力学敏感。对于无源偏置扩散，相反方向的逃逸可以具有不同的分裂概率，而其条件首次通过时间分布保持相同。我们研究了当活性布朗粒子在两个吸收边界之间受恒定外力驱动时，这种关系如何变化。自推进打破了上坡和下坡首次通过时间分布的相等性，并修改了分裂概率。然而，两个方向路径系综仍通过空间反射精确相关，该反射将相同持续时间的下坡和上坡首次通过路径配对，同时保留其取向历史。一条路径与其反射伙伴的概率之对数比定义了一个路径依赖的不对称性泛函，并提供了两个系综之间的精确重加权。在对称半加权表示中，上坡和下坡首次通过时间分布对于任意取向持久性均重合。相同的路径关系还允许从更频繁采样的下坡轨迹中重建罕见的上坡统计。数值模拟证实了在所探索的偏置和持久性范围内的加权相等性，而微扰和渐近分析阐明了取向持久性如何产生未加权统计的方向不对称性。两个方向路径系综之间的精确关系表明，在其他非平衡首次通过问题中可能找到类似的基于对称性的重建协议。

英文摘要

First passage processes in active systems combine stochastic transport with self-propulsion and orientational persistence, making motion along and against an external bias sensitive to the internal active dynamics. For passive biased diffusion, opposite exits can have different splitting probabilities while their conditional first passage time distributions remain identical. We study how this relation changes for an active Brownian particle driven by a constant external force between two absorbing boundaries. Self-propulsion breaks the equality of the uphill and downhill first passage time distributions and modifies the splitting probabilities. Nevertheless, the two directional path ensembles remain exactly related by spatial reflection, which pairs downhill and uphill first passage paths of the same duration while preserving their orientational history. The log-ratio of the probabilities of a path and its reflected partner defines a path-dependent asymmetry functional and provides an exact reweighting between the two ensembles. In the symmetric half-weighted representation, the uphill and downhill first passage time distributions coincide for arbitrary orientational persistence. The same path relation also allows rare uphill statistics to be reconstructed from the more frequently sampled downhill trajectories. Numerical simulations confirm the weighted equality across the explored bias and persistence regimes, while perturbative and asymptotic analyses clarify how orientational persistence produces the directional asymmetry of the unweighted statistics. The exact relation between the two directional path ensembles suggests that similar symmetry-based reconstruction protocols may be found in other nonequilibrium first-passage problems.

发表机构

• Universidade de Lisboa（里斯本大学）
• Hiroshima University（广岛大学）
• Charles University（查理大学）

机构由 AI 辅助整理，请以论文原文为准。