Uphill migration in coupled driven particle systems

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.