Thermodynamics and stochastic dynamics of transport in confined media

We show how a probabilistic interpretation of non-equilibrium thermodynamics, based on the assumption of local equilibrium at the mesoscale, can be used to analyze the stochastic dynamics of entropy driven diffusion processes characterized by the presence of entropic barriers. This approach sets up a systematic method to study the effect of confinement on the transport properties, providing a derivation of a generalized Fick-Jacobs equation for the constrained dynamics of the mesoscopic degrees of freedom. It is shown that confinement originates an entropic bias which gives rise to a geometric rectification of non-equilibrium fluctuations and that entropic effects in transport can be controlled by means of the application of an external force.