The entropy production of an active particle in a box

Nitzan Razin

Published 2020-08-18Version 1

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 persistence length of the particle motion, suggesting that the behavior of entropy production rate and its derivative as a function of the control parameter may signify a qualitative behavior change in the physics of active systems, such as phase transitions.