  Diffusive transport of particles or, more generally, small objects is a
ubiquitous feature of physical and chemical reaction systems. In configurations
containing confining walls or constrictions transport is controlled both by the
fluctuation statistics of the jittering objects and the phase space available
to their dynamics. Consequently, the study of transport at the macro- and
nanoscales must address both Brownian motion and entropic effects. With this
survey we report on recent advances in the theoretical and numerical
investigation of stochastic transport occurring either in micro-sized
geometries of varying cross section or in narrow channels wherein the diffusing
particles are hindered from passing each other (single file diffusion). For
particles undergoing biased diffusion in static suspension media enclosed by
confining geometries, transport exhibits intriguing features such as (i) a
decrease of nonlinear mobility with increasing temperature or, also, (ii) a
broad excess peak of the effective diffusion above the free diffusion limit.
These paradoxical aspects can be understood in terms of entropic contributions
resulting from the restricted dynamics in phase space. If, in addition, the
suspension medium is subjected to external, time-dependent forcing,
rectification or segregation of the diffusing Brownian particles becomes
possible. Likewise, the diffusion in very narrow, spatially modulated channels
gets modified via contact particle-particle interactions, which induce
anomalous sub-diffusion. The effective sub-diffusion constant for a driven
single file also develops a resonance-like structure as a function of the
confining coupling constant.
