The problem of diffusion in quasi-one-dimensional structures (tubes and channels) of varying cross section can be formulated to study the transport of particles in zeolites, soils, and other porous materials, in membrane channels and nanotubes, and also in a number of other physicochemical and biological processes [1,2]. The interest in this problem is caused by the advances in creating new materials and the significant progress in experimental research. The variation of the shape of a tube along its axis affects the space accessible for diffusion. The thus induced dependence of the entropy of a particle on its position determines the physics of the problem: tube expansions act as entropy wells and tube constrictions do as entropy barriers.
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