Statistical thermodynamics of nonequilibrium processes

Joel Keizer

This book provides an introduction to the modern statistical theory of nonequilibrium thermodynamics, based on a synthesis of the statistical thermodynamics of Onsager and the kinetic molecular theory of Boltzmann. Topics featured in the initial chapters include an introduction to stochastic processes and Brownian motion, the linear statistical theory of irreversible process, fluctuations in chemical reactions, and the Boltzmann equation. Using the author's canonical representation for the rates of elementary processes, the book develops the statistical thermodynamics of molecular process in a form that is useful for systems close to or far from equilibrium. Molecular noise arising from chemical reactions, electrochemical process, ion channels in membranes, hydrodynamics, and molecular collisions are treated in a unified way. The final chapters focus on the way in which nonlinear molecular mechanisms give rise to steady states, critical points, oscillations, and chaos, including the thermodynamic theory of steady states and its relationship to molecular fluctuations and linear stability. Broadly applicable to dynamical problems in chemistry, physics, and biophysics, the book should be accessible to graduate students, faculty, and other researchers in the physical sciences and engineering.

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  • 1 Ensembles and Stochastic Processes.- 1.1. The Mechanical Description of Matter.- 1.2. Macroscopic Descriptions and Contractions.- 1.3. Stochastic Processes and Physical Ensembles.- 1.4. Brownian Motion and the Wiener Process.- 1.5. The Langevin Equation and Stochastic Integrals.- 1.6. White Noise.- 1.7. Solution of the Langevin Equation.- 1.8. Ornstein-Uhlenbeck Processes.- References.- 2 Irreversible Processes: The Onsager and Boltzmann Pictures.- 2.1. Introduction.- 2.2. The Linear Laws.- 2.3. Entropy, Dissipation, Fluxes, and Forces.- 2.4. The Hydrodynamic Level of Description.- 2.5. Symmetry of the Two-Time Correlation Function and the Reciprocal Relations.- 2.6. Fluctuations in the Onsager Theory.- 2.7. The Boltzmann Equation.- 2.8. The H-Theorem.- 2.9. u-Space Averages and the Maxwell Distribution.- 2.10. Conservation Equations.- 2.11. Uniting the Onsager and Boltzmann Pictures.- References.- 3 Elementary Processes and Fluctuations.- 3.1. Introduction.- 3.2. The Stochastic Description of the Boltzmann Equation.- 3.3. The Fluctuating Boltzmann Equation.- 3.4. Elementary Chemical Reactions.- 3.5. The Canonical Form.- 3.6. Stochastic Theory of Chemical Reactions at the Thermodynamic Level of Description.- 3.7. Conservation Conditions and the Progress Variables.- 3.8. Thermodynamics of Chemical Equilibria.- References.- 4 Mechanistic Statistical Theory of Nonequilibrium Thermodynamcis.- 4.1. Introduction.- 4.2. The Canonical Theory.- 4.3. Solution of the Fokker-Planck Equation.- 4.4. Fluctuations and Dissipation.- 4.5. Thermodynamic Properties of the Canonical Theory.- 4.6. Equivalence to the Onsager Theory at Equilibrium.- 4.7. The Master Equation Formulation.- 4.8. Stochastic Diffusion Processes.- References.- 5 Thermodynamic-Level Description of Chemical, Electrochemical, and Ion Transport Mechanisms.- 5.1. Ionic Conduction Noise in Solution.- 5.2. The Feher-Weissman Experiment.- 5.3. The General Linear Mechanism.- 5.4. Bimolecular Isomerization.- 5.5. Continuously Stirred Tank Reactors and Molecule Reservoirs.- 5.6. Electrode Processes.- 5.7. Fluctuations Caused by Electrochemical Reactions.- 5.8. Ion Transport through Biological Membranes.- 5.9. Simulation of Fluctuations.- References.- 6 The Hydrodynamic Level of Description.- 6.1. Diffusion in an Isotropic Medium.- 6.2. Density Fluctuations Caused by Diffusion.- 6.3. Heat Conduction and Thermal Diffusion.- 6.4. Viscous Fluids: The Canonical Form.- 6.5. Fluctuating Hydrodynamics.- 6.6. Chemical Reactions and Diffusion.- 6.7. Quasi-elastic Scattering Theory.- 6.8. Light Scattering in a Thermal Gradient.- 6.9. Local versus Nonlocal Fluctuations.- References.- 7 Nonequilibrium Steady States.- 7.1. Steady-State Ensembles.- 7.2. Stability of Steady States.- 7.3. Fluctuations at Steady States.- 7.4. Multiple Steady States in Chemically Reactive Systems.- 7.5. Critical Points.- 7.6. The Gunn Effect.- References.- 8 Thermodynamics and the Stability of Steady States.- 8.1. The Thermodynamic Stability of Equilibrium.- 8.2. Fluctuations and Stability at Steady States.- 8.3. Thermodynamic Functions at Steady State.- 8.4. Thermodynamic Properties of Steady States.- 8.5. Free Energy and the Electromotive Force.- 8.6. The Nonequilibrium EMF in a Stirred Tank Reactor.- References.- 9 Hierarchies and Contractions of the Description.- 9.1. Introduction.- 9.2. Contractions without Memory.- 9.3. Contraction of Stationary, Gaussian, Markov Processes.- 9.4. Derivation of the Hydrodynamic Level of Description from the Boltzmann Level.- 9.5. Evaluation of Transport Coefficients.- 9.6. Rate Constants for Rapid Bimolecular Chemical Reactions.- References.- 10 Nonstationary Processes: Transients, Limit Cycles, and Chaotic Trajectories.- 10.1. Introduction.- 10.2. Nonstationary Systems and Nonlinear Transients.- 10.3. Limit Cycle Oscillations.- 10.4. Fluctuations on Limit Cycles.- 10.5. Chaotic Trajectories.- 10.6. Chaos in Complex Systems.- 10.7. Molecular Fluctuations versus Deterministic Chaos.- References.

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書名 Statistical thermodynamics of nonequilibrium processes
著作者等 Keizer, Joel
出版元 Springer-Verlag
刊行年月 c1987
ページ数 xiii, 506 p.
大きさ 25 cm
ISBN 3540965017
NCID BA00938540
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国