非马尔可夫系统中的快速状态再穿越动力学
Rapid state-recrossing kinetics in non-Markovian systems
AI总结：
该研究针对非马尔可夫系统中平均首次穿越时间的解读难题，通过模拟双稳态势中的一维广义朗之万方程，对比两种MFPT数值方法，揭示记忆诱导的快速状态再穿越的影响，证明分析非马尔可夫时间序列需考虑完整首次穿越分布。
摘要：
平均首次穿越时间（MFPT）是热激活势垒穿越过程中反应时间的一种标准度量。虽然对于满足马尔可夫动力学的系统，MFPT与唯象速率系数之间的关系已为人所知，但对于由非马尔可夫系统产生的实验和模拟时间序列数据，如何解读MFPT尚不明确。本文中，我们在双稳态势中模拟了一维广义朗之万方程（GLE），并比较了两种用于计算MFPT的相关数值方法：一种仅纳入后续状态间首次到达的信息，等价于计算等待时间（或称停留时间）；另一种纳入与给定势垒穿越事件相关的所有首次穿越信息，因此通常被用于增强数值采样。在马尔可夫极限下，两种方法是等价的。然而，当记忆时间显著时，两种方法给出的反应动力学结果差异极大。通过聚焦首次穿越分布，我们系统地揭示了记忆诱导的快速状态再穿越对MFPT的影响，并将其与多种其他反应时间的数值或理论描述进行了比较。总体而言，我们证明在分析非马尔可夫时间序列数据时，必须考虑完整的首次穿越分布，而非仅关注平均势垒穿越动力学。
英文摘要：
The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that satisfy Markovian dynamics, it is not clear how to interpret MFPTs for experimental and simulation time-series data generated by non-Markovian systems. Here, we simulate a one-dimensional generalized Langevin equation (GLE) in a bistable potential and compare two related numerical methods for evaluating MFPTs: one that only incorporates information about first arrivals between subsequent states and is equivalent to calculating the waiting time, or dwell time, and one that incorporates information about all first-passages associated with a given barrier-crossing event and is therefore typically employed to enhance numerical sampling. In the Markovian limit, the two methods are equivalent. However, for significant memory times, the two methods suggest dramatically different reaction kinetics. By focusing on first-passage distributions, we systematically reveal the influence of memory-induced rapid state-recrossing on the MFPTs, which we compare to various other numerical or theoretical descriptions of reaction times. Overall, we demonstrate that it is necessary to consider full first-passage distributions, rather than just the mean barrier-crossing kinetics when analyzing non-Markovian time series data.
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