  We use the mesoscopic nonequilibrium thermodynamics theory to derive the
general kinetic equation of a system in the presence of potential barriers. The
result is applied to the description of the evolution of systems whose dynamics
is influenced by entropic barriers. We analyze in detail the case of diffusion
in a domain of irregular geometry in which the presence of the boundaries
induces an entropy barrier when approaching the exact dynamics by a coarsening
of the description. The corresponding kinetic equation, named Fick-Jacobs
equation, is obtained, and its validity is generalized through the formulation
of a scaling law for the diffusion coefficient which depends on the shape of
the boundaries. The method we propose can be useful to analyze the dynamics of
systems at the nanoscale where the presence of entropy barriers is a common
feature.
