Entropy production of active particles in underdamped regime

TL;DR

This paper explores how inertia influences entropy production in active particles across various models, dimensions, and confinements, deriving exact results and revealing conditions for maximal entropy production.

Contribution

It introduces a simple expression linking entropy production to heat dissipation, derives new formulations from the Kramers equation, and provides exact results for unconfined and harmonic trap scenarios.

Findings

Entropy production is independent of temperature in unconfined and harmonic trap cases.

Maximum entropy production occurs at the oscillator's natural frequency.

Thermal fluctuations decrease entropy production in non-harmonic potentials.

Abstract

The present work investigates the effect of inertia on the entropy production rate $\Pi$ for all canonical models of active particles for different dimensions and the type of confinement. To calculate $\Pi$, the link between the entropy production and dissipation of heat rate is explored resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of $\Pi$ are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, $\Pi$ is independent of temperature. For the case of a harmonic trap, $\Pi$ attains a maximal value for $\tau = \omega^{-1}$ where $\tau$ is the persistence time and $\omega$ is the natural frequency of an oscillator. For active particles in 1D box, or other non-harmonic potentials, thermal fluctuations are found to reduce $\Pi$.