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. (paper: classical statistical mechanics, equilibrium and non-equilibrium)