The entropy production of an active particle in a box

TL;DR

This paper analytically investigates the steady state and entropy production of a run-and-tumble active particle confined in a one-dimensional box, revealing boundary layer effects and potential phase transition indicators.

Contribution

It provides an exact analytical solution for the steady state and entropy production rate of an active particle in a confined system, highlighting boundary layer phenomena and their relation to system size.

Findings

Boundary layer where particles accumulate near walls

Entropy production rate peaks at system boundaries

Derivative of entropy production rate indicates possible phase transition

Abstract

A run-and-tumble particle in a one dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the walls. The mesoscopic steady state entropy production rate of the system is derived from coupled Fokker-Planck equations with a linear reaction term, resulting in an exact analytic expression. The entropy production density is shown to peak at the walls. Additionally, the derivative of the entropy production rate peaks at a system size proportional to the length scale of the accumulation boundary layer, suggesting that the behavior of the entropy production rate and its derivatives as a function of the control parameter may signify a qualitative behavior change in the physics of active systems, such as phase transitions.