Mechanical pressure and work cycle of confined active Brownian particles

TL;DR

This paper derives an exact formula for the mechanical pressure of confined active Brownian particles across all conditions, revealing unique scaling behaviors and optimizing active engine efficiency.

Contribution

It provides a universal analytic expression for pressure in confined ABPs and explores the implications for active engine work and efficiency.

Findings

Pressure scales with Pe^2 in bulk and Pe under strong confinement.

Simulation results closely match the analytic pressure formula.

Active engine efficiency peaks at finite cycle periods, not infinitely slow.

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 Peclet number Pe and all confining scenarios. Our model reproduces the known scaling of bulk pressure with Pe^2 while in strong confinement pressure scales with Pe. 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.