# Thermodynamic uncertainty for run-and-tumble type processes

## TL;DR

This paper derives a new thermodynamic uncertainty bound for run-and-tumble processes applicable to both Markovian and non-Markovian systems, demonstrated on particle models and exclusion processes, requiring only run length statistics and entropy production.

## Contribution

It introduces a novel thermodynamic uncertainty bound specifically for run-and-tumble processes using renewal-reward theory, extending applicability to non-Markovian systems.

## Key findings

- Bound is tight over a broad parameter range.
- Requires only run length and entropy production statistics.
- Applicable to single-particle and collective models.

## Abstract

Thermodynamic uncertainty relations have emerged as universal bounds on current fluctuations in non-equilibrium systems. Here we derive a new bound for a particular class of run-and-tumble type processes using the mathematical framework of renewal-reward theory which can be applied to both Markovian and non-Markovian systems. We demonstrate the results for selected single-particle models as well as a variant of the asymmetric simple exclusion process with collective tumbles. Our bound is relatively tight for a broad parameter regime and only requires knowledge of the statistics of run lengths and the mean entropy production rate of tumbles.