Barbier-Chebbah A, Bénichou O, Voituriez R, Guérin T
Decision and Bayesian Computation, USR 3756 (C3BI/DBC) and Neuroscience Department CNRS UMR 3751, Institut Pasteur, Université de Paris, CNRS, 75015, Paris, France.
Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, 75005, Paris, France.
Nat Commun. 2024 Aug 28;15(1):7408. doi: 10.1038/s41467-024-50938-1.
The Kramers escape problem is a paradigmatic model for the kinetics of rare events, which are usually characterized by Arrhenius law. So far, analytical approaches have failed to capture the kinetics of rare events in the important case of non-Markovian processes with long-term memory, as occurs in the context of reactions involving proteins, long polymers, or strongly viscoelastic fluids. Here, based on a minimal model of non-Markovian Gaussian process with long-term memory, we determine quantitatively the mean FPT to a rare configuration and provide its asymptotics in the limit of a large energy barrier E. Our analysis unveils a correction to Arrhenius law, induced by long-term memory, which we determine analytically. This correction, which we show can be quantitatively significant, takes the form of a second effective energy barrier and captures the dependence of rare event kinetics on initial conditions, which is a hallmark of long-term memory. Altogether, our results quantify the impact of long-term memory on rare event kinetics, beyond Arrhenius law.
克莱默斯逃逸问题是罕见事件动力学的一个典型模型，这些罕见事件通常由阿仑尼乌斯定律表征。到目前为止，在涉及蛋白质、长聚合物或强粘弹性流体的反应中出现的具有长期记忆的非马尔可夫过程这一重要情况下，分析方法未能捕捉到罕见事件的动力学。在此，基于具有长期记忆的非马尔可夫高斯过程的一个最小模型，我们定量地确定了到达罕见构型的平均首次穿越时间，并在大能量势垒E的极限下给出其渐近形式。我们的分析揭示了由长期记忆引起的对阿仑尼乌斯定律的修正，我们通过解析方法确定了该修正。我们表明这种修正可能在数量上是显著的，它采取第二个有效能量势垒的形式，并捕捉了罕见事件动力学对初始条件的依赖性，这是长期记忆的一个标志。总之，我们的结果量化了长期记忆对罕见事件动力学的影响，超越了阿仑尼乌斯定律。
