Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model

Abstract

We study the distribution of the time-integrated current in an exactly-solvable toy model of heat conduction, both analytically and numerically. The simplicity of the model allows us to derive the full current large deviation function and the system statistics during a large deviation event. In this way we unveil a relation between system statistics at the end of a large deviation event and for intermediate times. Midtime statistics is independent of the sign of the current, a reflection of the time-reversal symmetry of microscopic dynamics, while endtime statistics do depend on the current sign, and also on its microscopic definition. We compare our exact results with simulations based on the direct evaluation of large deviation functions, analyzing the finite-size corrections of this simulation method and deriving detailed bounds for its applicability. We also show how the Gallavotti-Cohen fluctuation theorem can be used to determine the range of validity of simulation results.

13 pages, 7 figures, published version

References in corpus (18)

• The large deviation approach to statistical mechanics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Thermal conduction in classical low-dimensional lattices
• Fluctuation theorem for stochastic dynamics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Fluctuations in Stationary non Equilibrium States
• Direct evaluation of large-deviation functions
• Macroscopic current fluctuations in stochastic lattice gases
• Stochastic interacting particle systems out of equilibrium
• A numerical approach to large deviations in continuous-time
• A simple one-dimensional model of heat conduction which obeys Fourier's law
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Breakdown of Hydrodynamics in a Simple One-Dimensional Fluid
• Reply to comment on "Simple one-dimensional model of heat conduction which obeys Fourier's law"
• Strong Shock Waves and Nonequilibrium Response in a One-dimensional Gas: a Boltzmann Equation Approach

Cited by in corpus (48)

• Simulating rare events in dynamical processes
• 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
• Spontaneous Symmetry Breaking at the Fluctuating Level
• Population dynamics method with a multi-canonical feedback control
• Symmetries in Fluctuations Far from Equilibrium
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Dynamical phase transition for current statistics in a simple driven diffusive system
• Thermodynamics of currents in nonequilibrium diffusive systems: theory and simulation
• Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction
• Symmetry and the thermodynamics of currents in open quantum systems
• Harnessing symmetry to control quantum transport
• Large Fluctuations in Driven Dissipative Media
• Convergence of large deviation estimators
• Large deviations of Lyapunov exponents
• Finite size scaling of the dynamical free-energy in a kinetically constrained model
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Nonlinear driven diffusive systems with dissipation: fluctuating hydrodynamics
• Computing return times or return periods with rare event algorithms
• Order and symmetry-breaking in the fluctuations of driven systems
• Sampling rare events across dynamical phase transitions
• Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation
• Exact spatial correlations in single-file diffusion
• Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions: Numerical Approach in Continuous Time
• Efficient characterisation of large deviations using population dynamics
• Fluctuating hydrodynamics and mesoscopic effects of spatial correlations in dissipative systems with conserved momentum
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems
• Weak additivity principle for current statistics in d-dimensions
• Lattice models for granular-like velocity fields: Hydrodynamic limit
• Current fluctuations at a phase transition
• Fluctuations of the heat flux of a one-dimensional hard particle gas
• Lattice models for granular-like velocity fields: Finite-size effects
• Application of importance sampling to the computation of large deviations in non-equilibrium processes
• A framework for the direct evaluation of large deviations in non-Markovian processes
• The kinetic exclusion process: a tale of two fields
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems II: Full Counting Statistics
• Temporally correlated zero-range process with open boundaries: Steady state and fluctuations
• Probing local equilibrium in nonequilibrium fluids
• Scaling laws and bulk-boundary decoupling in heat flow
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Discreteness Effects in Population Dynamics
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Current fluctuations in the symmetric zero-range process below and at critical density
• Effective bandwidth of non-Markovian packet traffic
• Breakdown of the Finite-Time and -Population Scalings of the Large Deviation Function in the Large-Size Limit of a Contact Process
• Anomalous current fluctuations and mobility-driven clustering