Local entropy production rate of run-and-tumble particles

TL;DR

This paper investigates the local entropy production and flow in non-interacting run-and-tumble particles, deriving generic expressions and analyzing specific cases like space-dependent speed and external force fields.

Contribution

It provides new analytical expressions for entropy rates in active particles and compares them with numerical simulations in various scenarios.

Findings

Entropy rates depend only on the distribution and its derivatives in the stationary regime.

Analytical solutions are obtained for particles with space-dependent speed and external force fields.

Numerical simulations confirm the accuracy of the analytical approximations.

Abstract

We study the local entropy production rate and the local entropy flow in active systems composed of non-interacting run-and-tumble particles in a thermal bath. After providing generic time-dependend expressions, we focus on the stationary regime. Remarkably, in this regime the two entropies are equal and depend only on the distribution function and its spatial derivatives. We discuss in details two case studies, relevant to real situations. First, we analyze the case of space dependent speed,describing photokinetic bacteria, cosidering two different shapes of the speed, piecewise constant and sinusoidal. Finally, we investigate the case of external force fields, focusing on harmonic and linear potentials, which allow analytical treatment. In all investigated cases, we compare exact and approximated analytical results with numerical simulations.