Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states

Abstract

Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. The key result is the construction of the probability distribution for the underlying microscopic phase space trajectories. Three consequences of this result are then derived : the fluctuation theorem, the principle of maximum entropy production, and the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The accumulating empirical evidence for these results lends support to Jaynes' formalism as a common predictive framework for equilibrium and non-equilibrium statistical mechanics.

21 pages, 0 figures, minor modifications, version to appear in J. Phys. A. (2003)

References in corpus (2)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• The Fluctuation Theorem as a Gibbs Property

Cited by in corpus (87)

• Relativistic Fluid Dynamics: Physics for Many Different Scales
• Principal problems in Bose-Einstein condensation of dilute gases
• Thermodynamic Origin of Life
• Steady State of a Dissipative Flow-Controlled System and the Maximum Entropy Production Principle
• Rules for transition rates in nonequilibrium steady states
• Reconstruction methods for networks: the case of economic and financial systems
• Relativistic fluid dynamics: physics for many different scales
• How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?
• Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium
• Kirchhoff's Loop Law and the maximum entropy production principle
• Detailed balance has a counterpart in non-equilibrium steady states
• A discussion on maximum entropy production and information theory
• Rigorous meaning of McLennan ensembles
• Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions
• The climate system and the second law of thermodynamics
• Why did life emerge?
• Integral Biomathics: A Post-Newtonian View into the Logos of Bios (On the New Meaning, Relations and Principles of Life in Science)
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• One-dimensional transport of interacting particles: Currents, density profiles, phase diagrams and symmetries
• Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator
• Lectures on Probability, Entropy, and Statistical Physics
• Relaxed plasma equilibria and entropy-related plasma self-organization principles
• Planetary Atmospheres as Non-Equilibrium Condensed Matter
• A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
• Simultaneous Extrema in the Entropy Production for Steady-State Fluid Flow in Parallel Pipes
• Self-organization in foliated phase space: Construction of a scale hierarchy by adiabatic invariants of magnetized particles
• Reversibility, heat dissipation and the importance of the thermal environment in stochastic models of nonequilibrium steady states
• Nonequilibrium representative ensembles for isolated quantum systems
• Physical limits of wind energy within the atmosphere and its use as renewable energy: From the theoretical basis to practical implications
• Maximum caliber is a general variational principle for nonequilibrium statistical mechanics
• Hamiltonian formalism and path entropy maximization
• Present and Last Glacial Maximum climates as states of maximum entropy production
• The maximum entropy production principle and linear irreversible processes
• Statistical physics through the lens of real-space mutual information
• Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics
• Stochastic entropy production arising from nonstationary thermal transport
• Entropy production rates of the climate
• Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: Bénard Convection and Zonal flow
• Entropy Production and Coarse Graining of the Climate Fields in a General Circulation Model
• Maximum Caliber Inference and the Stochastic Ising Model
• Information Theory and Statistical Mechanics Revisited
• Entropy production and multiple equilibria: the case of the ice-albedo feedback
• Complexity of Networks (reprise)
• Formulations of moist thermodynamics for atmospheric modelling
• A Maximum Entropy Principle for inferring the Distribution of 3D Plasmoids
• Complexity of Networks
• Thermodynamics of MHD flows with axial symmetry
• Entropy production in systems with random transition rates
• Vertical Temperature Profiles at Maximum Entropy Production with a Net Exchange Radiative Formulation
• Why and How do Complex Systems Self-Organize at All? Average Action Efficiency as a Predictor, Measure, Driver, and Mechanism of Self-Organization
• Stationary state of a heated granular gas: fate of the usual H-functional
• Time-Energy and Time-Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations
• A First and Second Law for Nonequilibrium Thermodynamics: Maximum Entropy Derivation of the Fluctuation-Dissipation Theorem and Entropy Production Functionals
• Jaynes' Maximum Entropy Principle, Riemannian Metrics and Generalised Least Action Bound
• Single Member Selection in Ensemble Forecasting
• Physical portrayal of computational complexity
• Cooperative and collective effects in light of the maximum energy dissipation principle
• Phytoplankton temporal strategies increase entropy production in a marine food web model
• General formalism of non-equilibrium statistical mechanics, a path approach
• Comment on an information theoretic approach to the study of non-equilibrium steady states
• Entropy and Entropy Production in Some Applications
• On the variational framework employing optimal control for biochemical thermodynamics
• The second law, maximum entropy production and Liouville's theorem
• Entropy Production and Thermal Conductivity of A Dilute Gas
• Memory-induced long-range order in dynamical systems
• Entropy and Ionic Conductivity
• Fluctuations, Trajectory Entropy, and Ziegler's Maximum Entropy Production
• Probability as a physical motive
• Temperature Screening and Cross-Field Impurity Accumulation from a Thermodynamic Perspective
• Fluctuation Analysis of the Atmospheric Energy Cycle
• Entropy Production and Viscosity of A Dilute Gas
• An equivalence between a Maximum Caliber analysis of two-state kinetics and the Ising model
• The Laplace-Jaynes approach to induction
• Predictive use of the Maximum Entropy Production principle for Past and Present Climates
• Thermodynamics and Economics
• Minimisation of a Free-Energy-Like Potential for Non-Equilibrium Systems at Steady State
• Local temperature and chemical potential inside a mesoscopic device driven out of equilibrium
• Influence of probability density function of the passage time in the method of non-equilibrium statistical operator on non-equilibrium properties of the system
• Information Entropy Dynamics and Maximum Entropy Production Principle
• A road map for synthesizing the scaling patterns in ecology
• Intrinsic structure of liquid surface and capillary waves on the Density Functional Theory
• Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium
• Family of Nonequilibrium Statistical Operators and the Influence of the Past on the Present
• The thermodynamic hamiltonian for open systems
• Defining and finding lifelike entities with a lazy filter
• Microcanonical ensemble out of equilibrium
• Paths and stochastic order in open systems