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  • Open Access

Level 2.5 Large Deviations and Uncertainty Relations for Non-Markov Self-Interacting Dynamics

Francesco Coghi1,2,*, Amarjit Budhiraja3, and Juan P. Garrahan1,2

  • *Contact author: francesco.coghi@leicester.ac.uk
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Phys. Rev. Lett. 137, 197101 – Published 6 November, 2026

DOI: https://doi.org/10.1103/pt64-m494

Abstract

We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of “self-interacting” jump processes whose dynamics depends on the past through a functional of a state-dependent empirical observable. Exploiting a natural separation of timescales, and under the corresponding mixing conditions, we obtain the exact (so-called “level 2.5”) large deviation joint statistics of the empirical measure over configurations and of the empirical flux of transitions. As an application of this general framework, we derive explicit general bounds on the fluctuations of trajectory observables, generalizing to the non-Markovian case both thermodynamic and kinetic uncertainty relations. We illustrate our theory with simple examples, and discuss potential applications of these results.

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Level-2.5 large deviations and uncertainty relations for self-interacting jump processes: Tilting constructions and the emergence of timescale separation

Francesco Coghi and Juan P. Garrahan
Phys. Rev. E 114, 054112 (2026)

Article Text

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Outline

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Phys. Rev. Lett. 137, 197101– Published 6 November, 2026
  • Received 25 March 2026
  • Accepted 20 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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