The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and limited in validity to a neighborhood of equilibrium. In recent years it has been possible to extend the statistical theory of nonequilibrium processes to include nonlinear effects. The modern theory, as expounded in this book, is applicable to a wide variety of systems both close to and far from equilibrium. The theory is based on the notion of elementary molecular processes, which manifest themselves as random changes in the extensive variables characterizing a system. The theory has a hierarchical character and, thus, can be applied at various levels of molecular detail.

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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. µ-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. RateConstants 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.