Stationary uphill currents in locally perturbed zero-range processes
Uphill currents are observed when mass diffuses in the direction
of the density gradient. We study
this phenomenon in stationary conditions in the framework of locally
perturbed 1D Zero Range Processes (ZRP).
We show that the onset of currents flowing from the reservoir with smaller density to the one with larger density can be caused by a local asymmetry in the hopping rates on a
single site at the center of the lattice.
For fixed injection rates at the boundaries, we prove that
a suitable tuning of the asymmetry in the bulk may induce uphill diffusion at arbitrarily large, finite volumes.
We also deduce heuristically
the hydrodynamic behavior of the model and connect the local
asymmetry characterizing the ZRP dynamics to a matching condition relevant for the
macroscopic problem.