Fluctuations of entropy production of a run-and-tumble particle

TL;DR

This paper introduces a graphical method to compute any moment of entropy production in discrete and continuous run-and-tumble models, revealing non-Gaussian fluctuations in active particles relevant to biological systems.

Contribution

A novel graphical framework for calculating all moments of entropy production in generic discrete-state systems, applied to run-and-tumble dynamics.

Findings

Entropy production distribution deviates from Gaussian as states increase.

First three cumulants of entropy production computed analytically.

Framework extended to continuous state-space models.

Abstract

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of non-equilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several microorganisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach here presented might help uncover the features of non-equilibrium fluctuations of any current in biological systems operating out-of-equilibrium.