Coghi Francesco, Duvezin Romain, Wettlaufer John S
School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD United Kingdom.
Nordita, KTH Royal Institute of Technology and Stockholm University, SE-106 91 Stockholm, Sweden.
J Stat Phys. 2025;192(9):128. doi: 10.1007/s10955-025-03509-7. Epub 2025 Sep 13.
We study the first-passage dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein-Uhlenbeck process wherein the particle drift is modified by the empirical mean of its trajectory. This process maps onto a class of self-interacting diffusions. Using weak-noise large deviation theory, we calculate the leading order asymptotics of the time-dependent distribution of the particle position, derive the most probable paths that reach the specified position at a given time and quantify their likelihood via the action functional. We compute the feedback-modified Kramers rate and its inverse, which approximates the mean first-passage time, and show that the feedback accelerates dynamics by storing finite-time fluctuations, thereby lowering the effective energy barrier and shifting the optimal first-passage time from infinite to finite. Although we identify alternative mechanisms, such as slingshot and ballistic trajectories, we find that they remain sub-optimal and hence do not accelerate the dynamics. These results show how memory feedback reshapes rare event statistics, thereby offering a mechanism to potentially control first-passage dynamics.
我们研究了具有时间平均反馈的非马尔可夫随机过程的首次通过动力学，我们将其建模为一维奥恩斯坦 - 乌伦贝克过程，其中粒子漂移由其轨迹的经验均值修改。该过程映射到一类自相互作用扩散。使用弱噪声大偏差理论，我们计算了粒子位置随时间变化分布的主导阶渐近性，推导了在给定时间到达指定位置的最可能路径，并通过作用泛函量化了它们的可能性。我们计算了反馈修改的克莱默斯速率及其倒数，其近似平均首次通过时间，并表明反馈通过存储有限时间波动来加速动力学，从而降低有效能量势垒并将最优首次通过时间从无穷大转移到有限值。尽管我们确定了其他机制，如弹弓和弹道轨迹，但我们发现它们仍然不是最优的，因此不会加速动力学。这些结果展示了记忆反馈如何重塑罕见事件统计，从而提供了一种潜在控制首次通过动力学的机制。
