Stationary uphill currents in locally perturbed Zero Range Processes

TL;DR

This paper investigates stationary uphill currents in a one-dimensional Zero Range Process, demonstrating how local asymmetries in hopping rates can induce uphill diffusion even at large system sizes.

Contribution

It introduces a mechanism where local asymmetry in hopping rates causes uphill currents in ZRP, with proofs and heuristic analysis of the hydrodynamic limit.

Findings

Local asymmetry induces uphill currents.

Uphill diffusion can be controlled by tuning bulk asymmetry.

Results hold for arbitrarily large finite volumes.

Abstract

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.