Level 2.5 large deviations and uncertainty relations for non-Markov self-interacting dynamics

TL;DR

This paper develops a comprehensive framework for analyzing large deviations in non-Markovian self-interacting jump processes, deriving bounds on fluctuations and extending uncertainty relations beyond Markovian systems.

Contribution

It introduces an exact large deviation principle at level 2.5 for non-Markovian self-interacting dynamics, generalizing fluctuation bounds and uncertainty relations.

Findings

Derived explicit large deviation statistics for non-Markovian processes

Established generalized thermodynamic and kinetic uncertainty relations

Provided illustrative examples demonstrating the theory's applicability

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, 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, generalising 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.