Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries

Abstract

The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. In order to test its validity in the weakly asymmetric exclusion process with open boundaries, we use a numerical approach based on the density matrix renormalisation. With this technique, we determine the cumulant generating function of the current and the density profile corresponding to atypical currents in finite systems. We find that these converge to those predicted by the additivity principle. No evidence for dynamical phase transitions is found.

5 pages, 5 figures

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• A numerical approach to large deviations in continuous-time
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Exact Current Statistics of the ASEP with Open Boundaries
• Spontaneous Symmetry Breaking at the Fluctuating Level
• Symmetries in Fluctuations Far from Equilibrium
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Finite size scaling of current fluctuations in the totally asymmetric exclusion process
• Additivity Principle in High-dimensional Deterministic Systems
• Spontaneous symmetry breaking: variations on a theme

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• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
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