Macroscopic current fluctuations in stochastic lattice gases

Abstract

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach to density fluctuations developed in previous articles. More precisely, we derive large deviation estimates for the space--time fluctuations of the empirical current which include the previous results. Large time asymptotic estimates for the fluctuations of the time average of the current, recently established by Bodineau and Derrida, can be derived in a more general setting. There are models where we have to modify their estimates and some explicit examples are introduced.

4 pages, LaTeX, Changed content

Cited by in corpus (200)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Thermodynamic formalism for systems with Markov dynamics
• Direct evaluation of large-deviation functions
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter
• Stochastic interacting particle systems out of equilibrium
• Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
• Current fluctuations and transport efficiency for general Langevin systems
• Non equilibrium current fluctuations in stochastic lattice gases
• Universal cumulants of the current in diffusive systems on a ring
• A numerical approach to large deviations in continuous-time
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Exact Current Statistics of the ASEP with Open Boundaries
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Steady state statistics of driven diffusions
• Spontaneous Symmetry Breaking at the Fluctuating Level
• Cumulants and large deviations of the current through non-equilibrium steady states
• Effective interactions and large deviations in stochastic processes
• Chaotic properties of systems with Markov dynamics
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
• Optimizing active work: Dynamical phase transitions, collective motion, and jamming
• Symmetries in Fluctuations Far from Equilibrium
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Dynamical phase transition for current statistics in a simple driven diffusive system
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Open Quantum Symmetric Simple Exclusion Process
• Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction
• Large fluctuations and dynamic phase transition in a system of self-propelled particles
• Symmetry and the thermodynamics of currents in open quantum systems
• Current large deviation function for the open asymmetric simple exclusion process
• A nonequilibrium extension of the Clausius heat theorem
• Constraint driven condensation in large fluctuations of linear statistics
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Harnessing symmetry to control quantum transport
• Large deviation approach to nonequilibrium systems
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Large deviations conditioned on large deviations I: Markov chain and Langevin equation
• Time-symmetric fluctuations in nonequilibrium systems
• Singularities in large deviation functions
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• Large deviation approach to non equilibrium processes in stochastic lattice gases
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Large Fluctuations in Driven Dissipative Media
• Level 2 large deviation functionals for systems with and without detailed balance
• Decoherence and Full Counting Statistics in a Mach-Zehnder Interferometer
• Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Signatures of critical full counting statistics in a quantum-dot chain
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Field theories and exact stochastic equations for interacting particle systems
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Survival of a static target in a gas of diffusing particles with exclusion
• Building continuous time crystals from rare events
• Nonlinear driven diffusive systems with dissipation: fluctuating hydrodynamics
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium Steady States
• Computation of current cumulants for small nonequilibrium systems
• Equilibrium-like fluctuations in some boundary-driven open diffusive systems
• Statistics of large currents in the Kipnis-Marchioro-Presutti model in a ring geometry
• Bethe Ansatz for the Weakly Asymmetric Simple Exclusion Process and phase transition in the current distribution
• Universality in dynamical phase transitions of diffusive systems
• Vortices in the two-dimensional Simple Exclusion Process
• Sampling rare events across dynamical phase transitions
• The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation
• Non differentiable large-deviation functionals in boundary-driven diffusive systems
• Brownian asymmetric simple exclusion process
• Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems
• Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries
• Energy flux distribution in a two-temperature Ising model
• Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Void formation in diffusive lattice gases
• Cusp singularities in boundary-driven diffusive systems
• Trajectory phase transitions in non-interacting spin systems
• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Extreme Current Fluctuations in a Nonstationary Stochastic Heat Flow
• Non-Equilibrium Thermodynamics and Topology of Currents
• Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems
• Entropy production and its large deviations in an active lattice gas
• Dynamics of Repulsion Processes
• Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence
• Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
• Large deviations and optimal control forces for hard particles in one dimension
• Can the Macroscopic Fluctuation Theory be Quantized?
• Single-file transport in periodic potentials: The Brownian asymmetric exclusion process
• Large deviations of the empirical current in interacting particle systems
• Global Thermodynamics for Heat Conduction Systems
• Fluctuation relations for anisotropic systems
• Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case
• Observing symmetry-broken optimal paths of stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
• Weak additivity principle for current statistics in d-dimensions
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems
• Large deviations of the current in stochastic collisional dynamics
• Current fluctuations in stochastically resetting particle systems
• An atomic symmetry-controlled thermal switch
• Duality relations in single-file diffusion
• Effusion of stochastic processes on a line
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting
• Anomalies, absence of local equilibrium and universality in 1-d particles systems
• Stochastic Dynamics of Discrete Curves and Multi-type Exclusion Processes
• Current fluctuations in an interacting active lattice gas
• Current fluctuations at a phase transition
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Fluctuations of the heat flux of a one-dimensional hard particle gas
• Tricritical behavior in dynamical phase transitions
• Generalized disorder averages and current fluctuations in run and tumble particles
• Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• The kinetic exclusion process: a tale of two fields
• Large deviations of reaction fluxes
• Compact Waves in Microscopic Nonlinear Diffusion
• The exact phase diagram for a class of multispecies asymmetric exclusion processes
• Heterogeneity-induced large deviations in activity and (in some cases) entropy production
• Current distribution in systems with anomalous diffusion: renormalisation group approach
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Derivation of Stokes' Law from Kirkwood's Formula and the Green-Kubo Formula via Large Deviation Theory
• Spatial fluctuation theorem
• Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
• Singularities in Large Deviation Functionals of Bulk-Driven Transport Models
• Bernoulli variables, classical exclusion processes and free probability
• Statistics of the dissipated energy in driven diffusive systems
• Conditioned random walks and interaction-driven condensation
• 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
• Asymmetric fluctuation-relaxation paths in FPU models
• Dynamical fluctuations for periodically driven diffusions
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Solitons in fluctuating hydrodynamics of diffusive processes
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Current fluctuations in a semi-infinite line
• Anomalous System Size Dependence of Large Deviation Functions for Local Empirical Measure
• Single-file diffusion in spatially inhomogeneous systems
• Probing local equilibrium in nonequilibrium fluids
• Local structure of current fluctuations in diffusive systems beyond one dimension
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Dynamical Phase Transitions for Flows on Finite Graphs
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• KPZ fluctuations in finite volume
• Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder
• Macroscopic fluctuations theory of aerogel dynamics
• Nonequilibrium transport and phase transitions in driven diffusion of interacting particles
• Fluctuations of absorption of interacting diffusing particles by multiple absorbers
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Short-time large deviations of the spatially averaged height of a KPZ interface on a ring
• Large deviation generating function for energy transport in the Pauli-Fierz model
• Full absorption statistics of diffusing particles with exclusion
• Large deviations of a tracer position in the dense and the dilute limits of a single-file diffusion
• Thermodynamic Theory of Phase Transitions in Driven Lattice Gases
• Scaling laws and bulk-boundary decoupling in heat flow
• Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
• Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder
• Anomalous long-range correlations at a non-equilibrium phase transition
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Long-ranged correlations in large deviations of local clustering
• Uphill drift in the absence of current in single-file diffusion
• Importance Sampling for counting statistics in one-dimensional systems
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Programmable time crystals from higher-order packing fields
• Infinite family of universal profiles for heat current statistics in Fourier's law
• The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Fick's Law in Non-Local Evolution Equations
• Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
• An exactly solvable asymmetric $K$-exclusion process
• Large-time asymptotic of heavy tailed renewal processes
• Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting
• Full Current Statistics for a Disordered Open Exclusion Process
• Understanding random-walk dynamical phase coexistence through waiting times
• Current with "wrong" sign and phase transitions
• Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Critical behavior of a programmable time-crystal lattice gas
• Hydrodynamic limit of an exclusion process with vorticity
• Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas
• Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion
• Macroscopic fluctuation theory of interacting Brownian particles
• Noise driven phase transitions in eco-evolutionary systems
• Mechanical analysis of a dynamical phase transition for particles in a channel
• Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems
• Structure of the optimal path to a fluctuation
• The statistics of diffusive flux
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Stationary currents in long-range interacting magnetic systems
• Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions
• Current statistics and depinning transition for a one-dimensional Langevin process in the weak-noise limit