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DY: Fachverband Dynamik und Statistische Physik
DY 7: Focus Session: Large Deviations and Rare Events I
DY 7.3: Vortrag
Montag, 9. März 2026, 10:15–10:30, ZEU/0114
Large deviations and uncertainty relations for self-interacting jump processes — •Francesco Coghi1,2, Amarjit Budhiraja3, and Juan P. Garrahan1,2 — 1School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK — 2Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, UK — 3Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA
Self-interacting jump processes are stochastic systems where transition rates depend on the process' own empirical occupation measure -- that is, the time-averaged distribution of the states visited by the process -- introducing a feedback that breaks Markovianity. In this talk, I will present a large deviation framework for such systems. Specifically, I will derive the level-2.5 rate functional describing the joint fluctuations of occupation and flux, obtained via an exponential tilting construction extended to the non-Markovian setting. From this, I will show how memory modifies fluctuation bounds, leading to kinetic and thermodynamic uncertainty relations that generalise those of standard Markov processes. I will conclude with two examples that illustrate how feedback reshapes fluctuation-dissipation trade-offs: a minimal two-state model and a collective exploration process inspired by ant dynamics.
Keywords: Large deviations; Non-Markov processes; Self-interaction; Jump processes; Level 2.5