Vortices in the two-dimensional Simple Exclusion Process

Abstract

We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partialflux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed.

Revised version to appear in Journal of Statistical Physics. Minor corrections

References in corpus (13)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Dynamical ensembles in stationary states
• The Fluctuation Theorem as a Gibbs Property
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Macroscopic current fluctuations in stochastic lattice gases
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Non equilibrium current fluctuations in stochastic lattice gases
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Cumulants and large deviations of the current through non-equilibrium steady states
• Entropy production in nonequilibrium thermodynamics: a review
• Thermodynamic entropy production fluctuation in a two dimensional shear flow model
• Large deviations of the empirical current in interacting particle systems

Cited by in corpus (25)

• Macroscopic fluctuation theory
• Universal cumulants of the current in diffusive systems on a ring
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Current large deviations in a driven dissipative model
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Order and symmetry-breaking in the fluctuations of driven systems
• Sampling rare events across dynamical phase transitions
• Void formation in diffusive lattice gases
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• The kinetic exclusion process: a tale of two fields
• Melting of an Ising Quadrant
• Extreme current fluctuations of boundary-driven systems in the large-N limit
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results
• Full absorption statistics of diffusing particles with exclusion
• Fluctuations of absorption of interacting diffusing particles by multiple absorbers
• Current loops and fluctuations in the zero-range process on a diamond lattice
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• Current fluctuations in a stochastic system of classical particles with next-nearest-neighbor interactions
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Macroscopic fluctuation theory of interacting Brownian particles