Correlations of the density and of the current in non-equilibrium diffusive systems

Abstract

We use fluctuating hydrodynamics to analyze the dynamical properties in the non-equilibrium steady state of a diffusive system coupled with reservoirs. We derive the two-time correlations of the density and of the current in the hydrodynamic limit in terms of the diffusivity and the mobility. Within this hydrodynamic framework we discuss a generalization of the fluctuation dissipation relation in a non-equilibrium steady state where the response function is expressed in terms of the two-time correlations. We compare our results to an exact solution of the symmetric exclusion process. This exact solution also allows one to directly verify the fluctuating hydrodynamics equation.

arXiv comment26 pages, 4 figures, Submitted to J Stat Mech

References in corpus (29)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Fluctuations and response of nonequilibrium states
• Fluctuations in Stationary non Equilibrium States
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• A review of linear response theory for general differentiable dynamical systems
• Persistence exponents for fluctuating interfaces
• Off equilibrium dynamics and aging in unfrustrated systems
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model
• Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
• Symmetries in Fluctuations Far from Equilibrium
• Fluctuation relations in simple examples of non-equilibrium steady states
• The Lasting Effect of Initial Conditions on Single File Diffusion
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Entropy of Open Lattice Systems
• Fluctuation-Dissipation relations far from Equilibrium
• Large deviation function of a tracer position in single file diffusion
• Current fluctuations in systems with diffusive dynamics, in and out of equilibrium
• Non differentiable large-deviation functionals in boundary-driven diffusive systems
• A diffusive system driven by a battery or by a smoothly varying field
• From fluctuations in hydrodynamics to nonequilibrium thermodynamics
• Stationary non-equilibrium properties for a heat conduction model
• On a response formula and its interpretation

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• Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
• Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
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• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results
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• Hydrodynamics of a hard-core active lattice gas
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• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Anomalous current fluctuations and mobility-driven clustering
• Macroscopic fluctuation theory of interacting Brownian particles
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