Spectral theory for dynamical large deviations in non-Markov self-interacting processes

Francesco Coghi; Juan P. Garrahan

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arXiv · 2609.40329

Spectral theory for dynamical large deviations in non-Markov self-interacting processes

Francesco Coghi·Juan P. Garrahan

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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.

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Francesco Coghi, Juan P. Garrahan. 2026-09-30. Spectral theory for dynamical large deviations in non-Markov self-interacting processes. https://arxiv.org/abs/2609.40329

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