Current loops and fluctuations in the zero-range process on a diamond lattice

TL;DR

This paper investigates the zero-range process on a diamond lattice, analyzing current loops, fluctuations, and the Gallavotti-Cohen relation, revealing conditions for current loops and differences in fluctuation symmetry.

Contribution

It provides a detailed analysis of current loops and fluctuation relations in the zero-range process on a diamond lattice, including extensions to coupled diamonds.

Findings

Loops in mean current depend on boundary conditions

Gallavotti-Cohen relation holds for total current but not for partial currents

Coexistence of different mean current regimes in coupled diamond chains

Abstract

We study the zero-range process on a simple diamond lattice with open boundary conditions and determine the conditions for the existence of loops in the mean current. We also perform a large deviation analysis for fluctuations of partial and total currents and check the validity of the Gallavotti-Cohen fluctuation relation for these quantities. In this context, we show that the fluctuation relation is not satisfied for partial currents between sites even if it is satisfied for the total current flowing between the boundaries. Finally, we extend our methods to study a chain of coupled diamonds and demonstrate co-existence of mean current regimes.