Boundary-induced bulk phase transition and violation of Fick's law in two-component single-file diffusion with open boundaries

TL;DR

This paper investigates a two-component single-file diffusion model with open boundaries, revealing a boundary-induced phase transition and violations of Fick's law, supported by hydrodynamic theory and Monte Carlo simulations.

Contribution

It introduces a hydrodynamic framework for two-component single-file diffusion with boundary effects and uncovers a novel nonequilibrium phase transition and Fick's law violations.

Findings

Identification of a boundary-induced bulk phase transition.

Demonstration of Fick's law violations in the model.

Validation of theoretical predictions through Monte Carlo simulations.

Abstract

We study two-component single-file diffusion inside a narrow channel that at its ends is open and connected with particle reservoirs. Using a two-species version of the symmetric simple exclusion process as a model, we propose a hydrodynamic description of the coarse-grained dynamics with a self-diffusion coefficient that is inversely proportional to the length of the channel. The theory predicts an unexpected nonequilibrium phase transition for the bulk particle density as the external total density gradient between the reservoirs is varied. The individual particle currents do not in general satisfy Fick's first law. These results are confirmed by extensive dynamical Monte-Carlo simulations for equal diffusivities of the two components.