Local structure of current fluctuations in diffusive systems beyond one dimension

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.

18 pages, 7 figures

References in corpus (8)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Symmetries in Fluctuations Far from Equilibrium
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Factorised Steady States in Mass Transport Models on an Arbitrary Graph
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Spatial fluctuation theorem

Cited by in corpus (7)

• Order and symmetry-breaking in the fluctuations of driven systems
• Weak additivity principle for current statistics in d-dimensions
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Structure of the optimal path to a fluctuation
• Fluctuation Relations associated to an arbitrary bijection in path space