Mechanical pressure and work cycle of confined active Brownian particles

¹ Max–Planck–Institut für Intelligente Systeme - Heisenbergstr. 3, 70569 Stuttgart, Germany
² IV. Institut für Theoretische Physik, Universität Stuttgart - Pfaffenwaldring 57, 70569 Stuttgart, Germany
³ Helmholtz Institut Erlangen–Nürnberg for Renewable Energy (IEK–11), Forschungszentrum Jülich - Fürther Str. 248, 90429 Nürnberg, Germany
⁴ Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany

^(a) p.malgaretti@fz-juelich.de (corresponding author)

Received: 23 January 2021
Accepted: 23 March 2021

Abstract

We derive an analytic expression for the mechanical pressure of a generic one-dimensional model of confined active Brownian particles (ABPs) that is valid for all values of Péclet number and all confining scenarios. Our model reproduces the known scaling of bulk pressure with while in strong confinement pressure scales with . Our analytic results are very well reproduced by simulations of ABPs in 2D. We use the pressure formula to calculate both the work performed by an active engine and its efficiency. In particular, efficiency is maximized for work cycles with finite period and not in the limit of infinitely slow cycles as in thermodynamic engines.