The Statistical Mechanics of Irreversible Phenomena

Abstract

"This book provides a comprehensive and self-contained overview of recent progress in nonequilibrium statistical mechanics, in particular, the discovery of fluctuation relations and other time-reversal symmetry relations. The significance of these advances is that nonequilibrium statistical physics is no longer restricted to the linear regimes close to equilibrium, but extends to fully nonlinear regimes. These important new results have inspired the development of a unifying framework for describing both the microscopic dynamics of collections of particles, and the macroscopic hydrodynamics and thermodynamics of matter itself. The book discusses the significance of this theoretical framework in relation to a broad range of nonequilibrium processes, from the nanoscale to the macroscale, and is essential reading for researchers and graduate students in statistical physics, theoretical chemistry and biological physics"-- Cover -- Half-title -- Title page -- Copyright information -- Dedication -- Contents -- Preface -- 1 Thermodynamics -- 1.1 Generalities -- 1.2 Energy and Other Conserved Quantities -- 1.3 Entropy -- 1.3.1 Equilibrium Macrostates -- 1.3.2 Nonequilibrium Macrostates -- 1.4 Thermodynamics in Continuous Media -- 1.4.1 Balance Equations -- 1.4.2 Local Thermodynamic Equilibrium and Consequences -- 1.4.3 Equilibrium and Nonequilibrium Constitutive Relations -- 1.5 Hydrodynamics and Chemohydrodynamics -- 1.5.1 Hydrodynamics in One-Component Fluids -- 1.5.2 Chemohydrodynamics in Multicomponent Fluids 1.6 Hydrodynamic Modes of Relaxation to Equilibrium -- 1.6.1 Hydrodynamic Modes in One-Component Fluids -- 1.6.2 The Relaxation Modes in Diffusion-Reaction Systems -- 1.7 Nonequilibrium Steady States -- 1.7.1 From Local to Global Affinities -- 1.7.2 Diffusion -- 1.7.3 Ohm's Law for Electric Resistance -- 1.7.4 Electric Circuits -- 1.8 Reaction Networks -- 1.8.1 Flow Reactors -- 1.8.2 Stoichiometric Analysis of Reaction Networks -- 1.9 Dissipative Dynamics and Structures -- 1.10 Engines -- 1.10.1 Carnot Heat Engine -- 1.10.2 Isothermal Engines Working on Potential Differences -- 1.11 Open Issues 2 Statistical Mechanics -- 2.1 Introduction -- 2.2 Classical Mechanics -- 2.2.1 The Quantum Roots of Classical Mechanics -- 2.2.2 The Hamiltonian Function -- 2.2.3 Phase Space -- 2.2.4 Hamiltonian Dynamics -- 2.2.5 Existence and Uniqueness Theorem -- 2.2.6 Dynamical Stability or Instability -- 2.2.7 Symmetries of Hamiltonian Dynamics -- 2.3 Liouvillian Dynamics -- 2.3.1 Introduction to Statistical Ensembles -- 2.3.2 Liouville's Equation -- 2.3.3 Liouvillian Dynamics in Autonomous Systems -- 2.3.4 Time-Reversal Symmetry of Liouville's Equation -- 2.3.5 BBGKY Hierarchy -- 2.4 Ergodic Properties 2.4.1 Time Average -- 2.4.2 Ergodicity -- 2.4.3 Dynamical Mixing -- 2.4.4 Pollicott-Ruelle Resonances -- 2.5 Equilibrium Statistical Ensembles -- 2.5.1 Equilibrium Systems under Different Conditions -- 2.5.2 Detailed Balance -- 2.6 Nonequilibrium Statistical Ensembles -- 2.6.1 Symmetry Breaking by the Selection of Initial Conditions -- 2.6.2 Systems Evolving from Nonequilibrium Initial Macrostates -- 2.6.3 Systems in Nonequilibrium Steady Macrostates -- 2.7 Entropy -- 2.7.1 Coarse Graining -- 2.7.2 Interpretation -- 2.7.3 Coentropy -- 2.7.4 Further Coarse Graining 2.7.5 Dynamical Mixing and Entropy Time Evolution -- 2.7.6 Entropy Production -- 2.8 Linear Response Theory -- 2.8.1 Response Function and Dynamical Susceptibility -- 2.8.2 Electric Conductivity -- 2.8.3 Onsager-Casimir Reciprocal Relations -- 2.8.4 Fluctuation-Dissipation Theorem -- 2.9 Projection-Operator Methods -- 2.9.1 Zwanzig Projection-Operator Method -- 2.9.2 Mori Projection-Operator Method -- 3 Hydrodynamics -- 3.1 Nonequilibrium Statistical Mechanics and Hydrodynamics -- 3.2 Multicomponent Normal Fluids -- 3.2.1 Microscopic Densities and Balance Equations -- 3.2.2 Time Evolution