# Uphill migration in coupled driven particle systems

## TL;DR

This paper investigates uphill migration in coupled driven particle systems, revealing violations of Fick's law through a simple model of biased random walkers on rings, highlighting complex steady-state behaviors.

## Contribution

It introduces a minimal model of independent random walkers on coupled rings to explain uphill migration phenomena in driven particle systems.

## Key findings

- Uphill migration occurs depending on hopping dynamics.
- Violations of Fick's law are observed and explained.
- The model captures key features of nonuniform drive effects.

## Abstract

In particle systems subject to a nonuniform drive, particle migration is observed from the driven to the non--driven region and vice--versa, depending on details of the hopping dynamics, leading to apparent violations of Fick's law and of steady--state thermodynamics. We propose and discuss a very basic model in the framework of independent random walkers on a pair of rings, one of which features biased hopping rates, in which this phenomenon is observed and fully explained.