Non equilibrium steady states: fluctuations and large deviations of the density and of the current

Abstract

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow to calculate the fluctuations and large deviations of the density and of the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.

35 pages, 9 figures

References in corpus (12)

• Phase Coexistence in Driven One Dimensional Transport
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Fluctuation properties of the TASEP with periodic initial configuration
• A momentum conserving model with anomalous thermal conductivity in low dimension
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Work fluctuations for a Brownian particle between two thermostats
• Cumulants and large deviations of the current through non-equilibrium steady states
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• An exactly solvable model for driven dissipative systems
• Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process

Cited by in corpus (219)

• The large deviation approach to statistical mechanics
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Fluctuation theorems for stochastic dynamics
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Large Deviations in Single File Diffusion
• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation
• Symmetries in Fluctuations Far from Equilibrium
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Fluctuation relations and coarse-graining
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Response theory: a trajectory-based approach
• Large deviation function for entropy production in driven one-dimensional systems
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Exact anomalous current fluctuations in a deterministic interacting model
• Ballistic macroscopic fluctuation theory
• Exact short-time height distribution in 1D KPZ equation with Brownian initial condition
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• A matrix product solution for a nonequilibrium steady state of an XX chain
• Current fluctuations in stochastic systems with long-range memory
• Facilitated Asymmetric Exclusion
• Absence of Normal Fluctuations in an Integrable Magnet
• Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Exact description of quantum stochastic models as quantum resistors
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Survival of a static target in a gas of diffusing particles with exclusion
• Long range order in non-equilibrium interacting quantum spin chains
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Invariant quantities in shear flow
• Cumulants of the current in the weakly asymmetric exclusion process
• Asymmetric exclusion processes with constrained dynamics
• Inverse scattering solution of the weak noise theory of the Kardar-Parisi-Zhang equation with flat and Brownian initial conditions
• Learning nonequilibrium control forces to characterize dynamical phase transitions
• The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion
• Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
• Reinforcement learning of rare diffusive dynamics
• Universal anomalous fluctuations in charged single-file systems
• Exact spatial correlations in single-file diffusion
• Condensation of Fluctuations in and out of Equilibrium
• Generalized Exclusion Processes: Transport Coefficients
• Defect-induced phase transition in the asymmetric simple exclusion process
• Dynamical large deviations of linear diffusions
• Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Parallel Coupling of Symmetric and Asymmetric Exclusion Processes
• Lead Geometry and Transport Statistics in Molecular Junctions
• Generalised density profiles in single-file systems
• Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory
• Large deviations of currents in diffusions with reflective boundaries
• Correlations of the density and of the current in non-equilibrium diffusive systems
• Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems
• Work fluctuations for a Brownian particle driven by a correlated external random force
• Arrhenius law for interacting diffusive systems
• A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Variational design principles for nonequilibrium colloidal assembly
• On and beyond entropy production: the case of Markov jump processes
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Dynamical fluctuations in the Riesz gas
• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Large deviations in chaotic systems: exact results and dynamical phase transition
• Variational calculation of transport coefficients in diffusive lattice gases
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Can the Macroscopic Fluctuation Theory be Quantized?
• Trees and forests for nonequilibrium purposes: an introduction to graphical representations
• Observing symmetry-broken optimal paths of stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Exclusive Queueing Processes and their Application to Traffic Systems
• Time-averaged height distribution of the Kardar-Parisi-Zhang interface
• A large deviation theory perspective on nanoscale transport phenomena
• Exact solution of an integrable non-equilibrium particle system
• Jump-Drift and Jump-Diffusion Processes : Large Deviations for the density, the current and the jump-flow and for the excursions between jumps
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting
• Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• Dynamic Singularities in Cooperative Exclusion
• Tricritical behavior in dynamical phase transitions
• Balance network of asymmetric simple exclusion process
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval
• Large fluctuations in diffusion-controlled absorption
• Entropy production and fluctuation relations for a KPZ interface
• Generalized disorder averages and current fluctuations in run and tumble particles
• Graph-combinatorial approach for large deviations of Markov chains
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Energy and Heat Fluctuations in a Temperature Quench
• Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter
• Static large deviations of boundary driven exclusion processes
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks
• Heterogeneity-induced large deviations in activity and (in some cases) entropy production
• Local Detailed Balance : A Microscopic Derivation
• Dynamical phase transition in the occupation fraction statistics for non-crossing Brownian particles
• Effective estimation of entropy production with lacking data
• Local average height distribution of fluctuating interfaces
• Bernoulli variables, classical exclusion processes and free probability
• Isometric Uncertainty Relations
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• A nonequilibrium diffusion and capture mechanism ensures tip-localization of regulating proteins on dynamic filaments
• On the symmetry of current probability distributions in jump processes
• Relaxed hydrodynamic theory of electrically driven non-equilibrium steady states
• Conditioned random walks and interaction-driven condensation
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Tracer diffusion beyond Gaussian behavior: explicit results for general single-file systems
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Melting of an Ising Quadrant
• Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice
• Microcanonical conditioning of Markov processes on time-additive observables
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Exact Response Theory and Kuramoto dynamics
• Markov trajectories : Microcanonical Ensembles based on empirical observables as compared to Canonical Ensembles based on Markov generators
• Solitons in fluctuating hydrodynamics of diffusive processes
• Current fluctuations in the Dyson Gas
• Current fluctuations in a semi-infinite line
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Adaptive power method for estimating large deviations in Markov chains
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• From Vicious Walkers to TASEP
• Entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Integrability of two-species partially asymmetric exclusion processes
• Small noise asymptotic of the Gallavotti-Cohen functional for diffusion processes
• Lattice gases with a point source
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Interfacial and density fluctuations in a lattice model of motility-induced phase separation
• Current fluctuations in a partially asymmetric simple exclusion process with a defect particle
• Large deviations of a tracer position in the dense and the dilute limits of a single-file diffusion
• Large deviation generating function for energy transport in the Pauli-Fierz model
• Exclusion Processes with Avalanches
• Nonequilibrium steady states in coupled asymmetric and symmetric exclusion processes
• Experimental study of energy transport between two granular gas thermostats
• Long-range correlations in a simple stochastic model of coupled transport
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state
• Large deviations for out of equilibrium correlations in the symmetric simple exclusion process
• Hydrodynamics of a hard-core active lattice gas
• Steady state large deviations for one-dimensional, symmetric exclusion processes in weak contact with reservoirs
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• Importance Sampling for counting statistics in one-dimensional systems
• Full Counting Statistics and Fluctuation Theorem for the Currents in the Discrete Model of Feynman's Ratchet
• Symmetry shapes thermodynamics of macroscopic quantum systems
• Exclusion in Junction Geometries
• Structures of nonequilibrium fluctuations: dissipation and activity
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Cooperative transport with selective kinetic constraints
• Soft bounds on diffusion produce skewed distributions and Gompertz growth
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• The chemical birth-death process with Gillespie noise
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Tracer and current fluctuations in driven diffusive systems
• The Moving Born-Oppenheimer Approximation
• Realization of the open-boundary totally asymmetric simple exclusion process on a ring
• Positional information trade-offs in boundary-driven reaction-diffusion systems
• A two-line representation of stationary measure for open TASEP
• Complete Integrability of the Problem of Full Statistics of Nonstationary Mass Transfer in the Simple Inclusion Process
• Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
• Dynamic fluctuations of current and mass in nonequilibrium mass transport processes
• A combinatorial solution for the current fluctuations in the exclusion process
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Hydrostatics and dynamical large deviations of boundary driven gradient symmetric exclusion
• Emergence of the Gibbs ensemble as a steady state in Lindbladian dynamics
• Programmable time crystals from higher-order packing fields
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• Markov generators as non-hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and Singular Value Decompositions
• Current fluctuations in the symmetric zero-range process below and at critical density
• Fluctuating Hydrodynamics Describes Transport in Cellular Aggregates
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Inferring intermediate states by leveraging the many-body Arrhenius law
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Large-time asymptotic of heavy tailed renewal processes
• Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting
• An exactly solvable asymmetric $K$-exclusion process
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
• Stationary measure for six-vertex model on a strip
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Limits to positional information in boundary-driven systems
• Full distribution of the ground-state energy of potentials with weak disorder
• Nonequilibrium Phase Transition in a 2D Ferromagnetic Spins with Effective Interactions
• Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Universal and non-universal signatures in the scaling functions of critical variables
• Critical behavior of a programmable time-crystal lattice gas
• Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems
• From combinatorics to large deviations for the invariant measures of some multiclass particle systems
• Structure of the optimal path to a fluctuation
• Conditioning two diffusion processes with respect to their first-encounter properties
• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps
• Mechanical analysis of a dynamical phase transition for particles in a channel
• Anomalous current fluctuations and mobility-driven clustering
• Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion
• Symmetry Breaking of Current Response in Disordered Exclusion Processes
• Macroscopic fluctuation theory of interacting Brownian particles
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Density-dependent transport coefficients in two-dimensional cellular aggregates
• Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems
• A stochastic model solvable without integrability
• Limit fluctuations of stationary measure of totally asymmetric simple exclusion process with open boundaries on the coexistence line
• Dispersal and organization of polarized cells: non-linear diffusion and cluster formation without adhesion
• Lagrangian view of time irreversibility of fluid turbulence