  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.
