发表机构
University of Leicester; University of Nottingham（莱斯特大学; 诺丁汉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为非马尔可夫自相互作用过程建立动力学大偏差的谱理论，通过多尺度WKBJ拟设简化Feynman-Kac方程为特征值问题，并用双稳态East模型验证，提供高效计算框架。
AI 中文摘要
我们为非马尔可夫跳跃过程和非马尔可夫链中的动力学大偏差发展了谱理论，这些过程的动力学通过依赖于状态和跳跃的经验可观测量依赖于过去。我们证明了多尺度Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) 拟设将快速的构型弛豫与缓慢的记忆演化分离，将占据数和通量统计的Feynman-Kac方程简化为与Hamilton-Jacobi特征线耦合的新倾斜算子的特征值问题。这为量化广泛非马尔可夫系统中的涨落提供了一种计算高效的框架。我们用一个双稳态自诱导East模型说明了我们的通用结果。
英文摘要
We develop a spectral theory for dynamical large deviations in non-Markov jump processes and non-Markov chains, whose dynamics depends on the past through state- and jump-dependent empirical observables. We demonstrate that a multiscale Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) Ansatz separates fast configurational relaxation from slow memory evolution, reducing the Feynman--Kac equation for occupation and flux statistics to an eigenvalue problem for a new tilted operator coupled to Hamilton--Jacobi characteristics. This provides a computationally efficient framework for quantifying fluctuations in a broad class of non-Markovian systems. We illustrate our general results with a bistable self-induced East model.
Comments6 pages, 2 figures
