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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

  • School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom

  • *Contact author: francesco.coghi@leicester.ac.uk
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Phys. Rev. E 114, 054112 – Published 6 November, 2026

DOI: https://doi.org/10.1103/vhv8-tcrs

Abstract

Self-interacting jump processes (SIJPs) describe systems with non-Markovian stochastic dynamics in which transition rates depend on empirical observables of the process, which gives rise to long-range memory and feedback. We derive the “level-2.5” large deviation (LD) principle governing the joint fluctuations of empirical occupation measure and the flux matrix for a broad class of SIJPs with general functional dependence on an empirical observable. The derivation is based on an exponential tilting construction and reveals a separation between a faster timescale of the microscopic dynamics and a slower timescale of the memory-driven evolution of transition rates, which is expressed through an exponentially discounted LD rate functional. Using this variational framework, we derive kinetic and thermodynamic uncertainty relations that extend classical Markovian bounds to non-Markovian systems and illustrate their performance with simple examples.

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

Francesco Coghi, Amarjit Budhiraja, and Juan P. Garrahan
Phys. Rev. Lett. 137, 197101 (2026)

Article Text

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Phys. Rev. E 114, 054112– Published 6 November, 2026
  • Received 25 March 2026
  • Accepted 21 October 2026
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