Entropic transport - A test bed for the Fick-Jacobs approximation

TL;DR

This paper investigates the biased diffusive transport of particles in irregular structures, testing the Fick-Jacobs approximation against simulations, and explores how entropic barriers influence non-equilibrium transport and fluctuation relations.

Contribution

It evaluates the validity of the Fick-Jacobs approximation for modeling entropic transport in complex geometries through comparison with detailed simulations.

Findings

Fick-Jacobs approximation accurately describes particle dynamics in certain regimes.

Entropic barriers significantly affect transport properties and fluctuation relations.

Non-equilibrium transport shows violations of the fluctuation-dissipation theorem at moderate to strong biases.

Abstract

Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called Fick-Jacobs approximation, yielding an effective one-dimensional stochastic dynamics. Accordingly, the elimination of transverse, equilibrated degrees of freedom stemming from geometrical confinements and/or bottlenecks cause entropic potential barriers which the particles have to overcome when moving forward noisily. The applicability and the validity of the reduced kinetic description is tested by comparing the approximation with Brownian dynamics simulations in full configuration space. This non-equilibrium transport in such quasi-one-dimensional irregular structures implies for moderate-to-strong bias a characteristic violation of the Sutherland-Einstein fluctuation-dissipation relation.