Abstract

I will discuss recent work on the validity of the so-called first-passage duality for run-and-tumble motion (and other renewal-type processes) in both discrete and continuous settings. This symmetry relates the distributions of first-passage times to absorbing boundaries in the directions of and against a bias. It can generally be derived for entropy-like quantities but does not necessarily hold for currents of active run-and-tumble particles; indeed the violation can have a non-trivial dependence on the tumbling rate. I will give conditions for the duality to be restored asymptotically (in the limit of a large barrier distance) and highlight connections to the Gallavotti-Cohen fluctuation relation and the method of images. In addition, I will discuss finite-size corrections to the asymptotic behaviour with the aid of simple models amenable to exact calculations and/or perturbation analysis for small tumbling rate.

Based on https://arxiv.org/abs/2505.24483 with Yonathan Sarmiento, Benjamin Walter, Debraj Das, Samvit Mahapatra, and Édgar Roldán.