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

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.

Major revision with new section on diamond chain, to appear in JSTAT

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Cited by in corpus (5)

• Dynamical large deviations of linear diffusions
• Fluctuation relations without uniform large deviations
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Particle current fluctuations in a particle-nonconserving process