Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Coghi, Francesco, Garrahan, Juan P.
Institution: University of Nottingham
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215034299