Fractional Fick's law for the boundary driven exclusion process with long jumps

TL;DR

This paper derives a fractional Fick's law and hydrostatics for a one-dimensional exclusion process with long jumps, modeling particle transport between reservoirs with different densities.

Contribution

It introduces a fractional Fick's law framework for exclusion processes with long jumps, extending classical models to non-local dynamics.

Findings

Derived fractional Fick's law for long jump exclusion process

Established fractional hydrostatics in contact with reservoirs

Extended classical diffusion models to non-local interactions

Abstract

A fractional Fick's law and fractional hydrostatics for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities on the left and on the right are derived.