Exact probability function for bulk density and current in the asymmetric exclusion process

Abstract

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques, and by introducing a modified version of the original operator algebra. As a byproduct of these considerations we also arrive at a novel and very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.

10 pages, 4 figures

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Cited by in corpus (10)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Direct evaluation of large-deviation functions
• Cumulants and large deviations of the current through non-equilibrium steady states
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Statistics of current activity fluctuations in asymmetric flow with exclusion
• Sampling rare fluctuations of height in the Oslo ricepile model
• Numerical Estimation of the Current Large Deviation Function in the Asymmetric Simple Exclusion Process with Open Boundary Conditions
• Current-activity versus local-current fluctuations in driven flow with exclusion