The Exclusion Process: A paradigm for non-equilibrium behaviour

Abstract

In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us with a unified description of many physical situations. These functions are expected to play, for systems far from equilibrium, a role akin to that of the thermodynamic potentials. These concepts will be illustrated by exact solutions of the Asymmetric Exclusion Process, a paradigm for non-equilibrium statistical physics.

Proceedings of the 13th International Summer School on Fundamental Problems in Statistical Physics (Edited by Marco Baiesi, Enrico Carlon and Andrea Parmeggiani)

References in corpus (16)

• 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
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Macroscopic fluctuation theory for stationary non equilibrium states
• Exact Large Deviation Function in the Asymmetric Exclusion Process
• A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Exact Current Statistics of the ASEP with Open Boundaries
• Exact Results for the Asymmetric Simple Exclusion Process with a Blockage
• Cumulants and large deviations of the current through non-equilibrium steady states
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Tree structures for the current fluctuations in the exclusion process

Cited by in corpus (79)

• Introduction to dynamical large deviations of Markov processes
• Stochastic resetting in interacting particle systems: A review
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Nonlinear response and emerging nonequilibrium micro-structures for biased diffusion in confined crowding environments
• Le Chatelier principle for out of equilibrium and boundary driven systems : application to dynamical phase transitions
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Universality in dynamical phase transitions of diffusive systems
• Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model
• Universal anomalous fluctuations in charged single-file systems
• Nonequilibrium fluctuations and enhanced diffusion of a driven particle in a dense environment
• Rise and fall, and slow rise again, of operator entanglement under dephasing
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Dynamical large deviations of linear diffusions
• Generalised density profiles in single-file systems
• Absolute negative mobility of an active tracer in a crowded environment
• Optimal sampling of dynamical large deviations via matrix product states
• Arrhenius law for interacting diffusive systems
• Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Speed-Dispersion Induced Alignment : a 1D model inspired by swimming droplets experiments
• The bosonic skin effect: boundary condensation in asymmetric transport
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Microscopic theory for the diffusion of an active particle in a crowded environment
• Inflow rate, a time-symmetric observable obeying fluctuation relations
• Can the Macroscopic Fluctuation Theory be Quantized?
• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems
• Duality relations in single-file diffusion
• Large deviations in the symmetric simple exclusion process with slow boundaries
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
• Deterministic Bethe state preparation
• Joint distribution of currents in the symmetric exclusion process
• Bernoulli variables, classical exclusion processes and free probability
• Flagellar length control in biflagellate eukaryotes: time-of-flight, shared pool, train traffic and cooperative phenomena
• Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes
• Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond
• Solitons in fluctuating hydrodynamics of diffusive processes
• KPZ fluctuations in finite volume
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Attraction and condensation of driven tracers in a narrow channel
• A Multispecies Exclusion Model Inspired By Transcriptional Interference
• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• A Multispecies Exclusion Process with Fusion and Fission of Rods: a model inspired by Intraflagellar Transport
• A Biologically Motivated Asymmetric Exclusion Process: interplay of congestion in RNA polymerase traffic and slippage of nascent transcript
• Sloppy Gear Mechanism for Coupled Stochastic Transportation: from anti-equilibrium flow to infinite selectivity
• TASEP Speed Process: An Effective Medium Approach
• Semi-infinite simple exclusion process: from current fluctuations to target survival
• Importance Sampling for counting statistics in one-dimensional systems
• Multi species asymmetric simple exclusion process with impurity activated flips
• Monitored Fluctuating Hydrodynamics
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Imitating non-equilibrium steady states using time-varying equilibrium force in many-body diffusive systems
• Diffusion and entanglement in open quantum systems
• Glauber's Ising chain between two thermostats
• Tracer and current fluctuations in driven diffusive systems
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• Recurrence dynamics of particulate transport with reversible blockage: from a single channel to a bundle of coupled channels
• Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems
• A biologically motivated three-species exclusion model: effects of leaky scanning and overlapping genes on initiation of protein synthesis
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Inferring intermediate states by leveraging the many-body Arrhenius law
• Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
• Synchronized shocks in an inhomogeneous exclusion process
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems
• Current reversals in driven lattice gases and Brownian motion
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Macroscopic fluctuation theory of interacting Brownian particles
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Boundary layers, transport and universal distribution in boundary driven active systems