Active particles in a tube: a generalized entropy potential approach

We study the transport of self-propelled noninteracting active Brownian particles (ABPs) and run-and-tumble particles (RTPs) in long tubes of varying widths. Using a moment expansion, we construct a generalized Fick-Jacobs framework for the active particles when the tube width is large and slowly varying. We show that the variation of the particle density along the tube is well described by a one-dimensional generalized entropy potential. This potential resembles its passive counterpart, albeit with an effective temperature and an effective tube width that are renormalized by the activity. Our generalized entropy potential approach allows us to predict the steady-state density distribution along the tube as well as the mean escape time out of a spindle chamber. Finally, we show how to account for the emergence of spontaneous ratchet flows in asymmetric channel by including higher-order corrections neglected in the effective entropy potential approach.