竞争性首达事件中记忆效应的证据与量化
Evidence and quantification of memory effects in competitive first passage events
AI总结：
本研究提出解析方法计算一维非马尔可夫高斯过程的分裂概率，揭示其受首达后非平衡轨迹控制，并推广至d维，为复杂介质中竞争事件研究开辟新路径。
摘要：
分裂概率量化了竞争性事件中给定结果的可能性。这一随机游走理论的关键可观测量，历史上作为赌徒破产问题引入，对于无记忆（马尔可夫）过程已被充分理解。然而，在诸如聚合物流体等复杂系统中，粒子的运动通常应被描述为具有记忆的过程，而此类过程的分裂概率在解析上鲜有表征。在此，我们引入一种解析方法，针对两个目标的情形，为具有平稳增量的各向同性一维非马尔可夫高斯过程提供分裂概率。该分析表明，分裂概率受首次通过后观测到的非平衡轨迹控制。这在粘弹性流体的典型实验反应方案中得到了直接证实。这些结果被推广到大型受限体积中的$d$维过程，为研究复杂介质中的竞争性事件开辟了路径。
英文摘要：
Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian) processes. However, in complex systems such as polymer fluids, the motion of a particle should typically be described as a process with memory, for which splitting probabilities are much less characterized analytically. Here, we introduce an analytical approach that provides the splitting probabilities for one-dimensional isotropic non-Markovian Gaussian processes with stationary increments, in the case of two targets. This analysis shows that splitting probabilities are controlled by the out of equilibrium trajectories observed after the first passage. This is directly evidenced in a prototypical experimental reaction scheme in viscoelastic fluids. These results are extended to $d$-dimensional processes in large confining volumes, opening a path towards the study of competitive events in complex media.
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