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DY: Fachverband Dynamik und Statistische Physik
DY 7: Focus Session: Large Deviations and Rare Events I
DY 7.10: Vortrag
Montag, 9. März 2026, 12:30–12:45, ZEU/0114
Optimal escape processes of run-and-tumble particles — Karthik Cheruvary2, •Rafael Diaz Hernandez Rojas1, and Peter Sollich1 — 1University of Göttingen — 2IISER Pune
Run-and-tumble (RT) motion is a fundamental mode of self-propulsion observed across diverse biological systems from bacterial chemotaxis to immune cell migration. Modelling this non-equilibrium system is challenging due to the non-Gaussian noise governing the self-propulsion direction, θ. To address this, we investigate the trajectories of a particle confined by a potential in d=2 and subject to both thermal fluctuations and RT motion. We incorporate tumbling by modelling changes in θ as Poisson shot noise process with rate λ and generic distribution of angle changes, Δ. Employing a path-integral formalism in the weak noise limit, we derive exact equations of motion for all degrees of freedom, valid for arbitrary λ and distributions of Δ. This allows us to map the problem of finding the most likely escape trajectory to the minimisation of an appropriate action. Our analysis reveals that the effects of the non-Gaussian noise are more prominent in the limit of small λ, which corresponds to highly persistent RT motion. There, we show analytically that, regardless of the distribution of Δ, RT escape paths are exponentially more probable –exhibiting a lower action– than their active Brownian particle equivalent. The optimal RT trajectories are non-trivial and can exhibit discontinuities or very rapid changes in θ, implying that RT particles will exploit their tumbling ability to optimize escape from potential wells. We verify our theoretical predictions through extensive numerical simulations.
Keywords: Escape processes; Run-and-tumble motion; Non-Gaussian noise; path-integrals in stochastic processes