Local structure of current fluctuations in diffusive systems beyond one dimension

TL;DR

This paper investigates current fluctuations in two-dimensional diffusive systems using a lattice-based Markov process, revealing how geometry and local structures influence fluctuations and symmetry properties.

Contribution

It provides a detailed analysis of current fluctuations in 2D zero-range processes, highlighting the effects of lattice geometry and local current structures beyond one dimension.

Findings

Current fluctuations depend on lattice geometry (square vs. triangular).

Local current structures are linked to global fluctuation properties.

Spatial inhomogeneities affect fluctuation symmetry tests.

Abstract

In order to illuminate the properties of current fluctuations in more than one dimension, we use a lattice-based Markov process driven into a non-equilibrium steady state. Specifically, we perform a detailed study of the particle current fluctuations in a two-dimensional zero-range process with open boundary conditions and probe the influence of the underlying geometry by comparing results from a square and a triangular lattice. Moreover, we examine the structure of local currents corresponding to a given global current fluctuation and comment on the role of spatial inhomogeneities for the discrepancies observed in testing some recent fluctuation symmetries.