PreprintCC BY 4.0arXiv
Spectral theory for dynamical large deviations in non-Markov self-interacting processes
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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BibTeX
@misc{coghi2026spectral,
title = {{Spectral theory for dynamical large deviations in non-Markov self-interacting processes}},
author = {Francesco Coghi and Juan P. Garrahan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40329},
eprint = {2609.40329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40329},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral theory for dynamical large deviations in non-Markov self-interacting processes
AU - Francesco Coghi
AU - Juan P. Garrahan
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.40329
UR - https://arxiv.org/abs/2609.40329
AB - 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.
ER -