Kinetic equations for diffusion in the presence of entropic barriers

TLDR

The study derives a general kinetic equation for systems with potential barriers using mesoscopic nonequilibrium thermodynamics. The authors derive the Fick‑Jacobs equation for diffusion in irregular geometries, extending its validity with a scaling law for the diffusion coefficient that depends on boundary shape. The resulting kinetic equation is applied to describe systems influenced by entropic barriers, and the method is useful for analyzing nanoscale dynamics where such barriers are common.

Abstract

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 a 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 the 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.