Schematic representation of a tube of alternating diameter (panel (a)) and corresponding dimensionless entropy potential (panel (b)). The tube consists of alternating wide and narrow sections of radii R and a whose lengths are equal to lw and ln, respectively. The dimensionless entropy potential, βU(x) = 2 ln (R/r(x)), is equal to zero and 2 ln (R/a) in the wide and narrow sections of the tube, respectively. At the boundaries separating the two sections the potential make a jump, βΔU = 2 ln (R/a).