Equilibrium and Nonequilibrium Statistical Mechanics 0471046000, 9780471046004

Table of contents :
PREFACE
CONTENTS
PART 1. GENERAL CONCEPTS OF STATISTICAL MECHANICS
Chapter 1. Review of Hamiltonian Dynamics
1.1. Individual and Global Behavior
1.2. Hamiltonian Description of Classical Mechanics
1.3. Hamiltonian Description of Quantum Mechanics
1.4. Pure States in Quantum Mechanics: Bosons and Fermions
1.5. The Second Quantization Formalism
Chapter 2. Statistical Ensembles
2.1. Macroscopic Physics and Microscopic Physics
2.2. Classical Ensembles: The Phase-Space Distribution Function
2.3. Quantum Ensembles: The von Neumann Density Operator
2.4. Hamiltonian and Liouvillian of a System of Interacting Particles
Chapter 3. Reduced Distribution Functions
3.1. The Classical Distribution Vector
3.2. The Principle of Macroscopic Equivalence
3.3. The Thermodynamic Limit
3.4. Evolution in Time of the Classical Distribution Vector
3.5. Homogeneous and Inhomogeneous Systems: Correlations in Classical Systems
3.6. The Quantum Distribution Vector: The Wigner Functions
3.7. Evolution in time of the Quantum Distribution Vector
3.8. Special Properties of Wigner Functions: Quantum Correlations
PART 2. EQUILIBRIUM STATISTICAL MECHANICS
Chapter 4. Equilibrium Ensembles and Thermodynamics
4.1. Equilibrium Solutions of the Liouville Equation
4.2. The Microcanonical Ensemble
4.3. The Canonical Ensemble
4.4. Connection Between Statistical Mechanics and Thermodynamics
4.5. The Grand Canonical Ensemble
4.6. Equivalence of the Equilibrium Ensembles: Fluctuations
*4.7. Dynamics and Thermodynamics: Existence of the Thermodynamic Limit
Appendix: The Method of the Most Probable Distribution
Chapter 5. Equilibrium Properties of Ideal Systems
5.1. Definition of Ideal Systems
5.2. Ideal Systems in the High-Temperature Limit: The Boltzmann Gas
5.3. Molecular Structure and Thermodynamics
5.4. Ideal Systems of Bosons or Fermions
5.5. The Bose-Einstein and the Fermi-Dirac Distributions
5.6. Highly Degenerate Ideal Fermi Gases
5.7. Highly Degenerate Ideal Bose Gases
Chapter 6. Slightly Nonideal Systems in Equilibrium
6.1. Perturbation Expansions in Statistical Mechanics
6.2. The λ Expansion of the Configuration Integral
6.3. The λ Expansion of the Free Energy
6.4. The Density Expansion of the Free Energy: The Virial Coefficients
6.5. Classical Plasmas in Equilibrium
Chapter 7. Reduced Distribution Functions in Equilibrium
7.1. Basic Definitions
7.2. Thermodynamic Quantities Expressed in Terms of Reduced Distribution Functions
7.3. Reduced Distribution Functions of Ideal Systems in Equilibrium
7.4. Equilibrium Hierarchy for the Reduced Distribution Functions
7.5. Connection Between the Partition Function and the Reduced Distribution Functions
Chapter 8. Dense Fluids in Equilibrium
8.1. Pair Correlation Function and Scattering Phenomena
8.2. Density Expansion of the Pair Distribution Function
8.3. The Percus-Yevick and the Hypernetted-Chains Equation
*8.4. Solution of the Percus-Yevick Equation for Hard Spheres
8.5. The Monte Carlo and the Molecular-Dynamics Method
8.6. Present State of the Theory of Dense Fluids
Chapter 9. Phase Transitions
9.1. Qualitative Description of Phase Transitions
9.2. Weiss' Mean Field Theory of Ferromagnetism
9.3. The van der Waals Theory of Condensation
*9.4. Weak Infinite-Range Interactions and the van der Waals-Maxwell Equation
9.5. Macroscopic Properties Near the Critical Point
9.6. Correlations Near the Critical Point
Chapter 10. Modern Theories of Critical Phenomena
10.1. Methods of Investigation of Critical Phenomena
10.2. Model Systems
10.3. Exponent Inequalities
10.4. The Scaling-Law Hypothesis
10.5. Kadanoff's Theory of the Scaling Laws
10.6. Wilson's Formulation of the Kadanoff Theory
10.7. The Renormalization-Group Equations and the Partition Function
10.8. Dimensionality as a Continuous Parameter
PART 3. NONEQUILIBRIUM STATISTICAL MECHANICS
Chapter 11. Intuitive Treatment of Nonequilibrium Phenomena
11.1. Introduction
11.2. Theory of the Brownian Motion: The Langevin Equation
11.3. Random Processes: The Fokker-Planck Equation
11.4. Dilute Gases: The Boltzmann Equation
11.5. Assumptions Made in the Derivation of the Boltzmann Equation
11.6. Homogeneous Weakly Coupled Gases: The Landau Equation
11.7. Inhomogeneous Plasmas: The Vlassov Equation
11.8. Connection Between the Landau and the Fokker-Planck Equations
Chapter 12. Kinetic Equations and Hydrodynamics
12.1. Moment Equations of a Kinetic Equation
12.2. Boltzmann's H Theorem and the Entropy Balance: Irreversibility and Dissipativity
12.3. The Collisional Invariants
12.4. The Hydrodynamical Balance Equations
12.5. The Phenomenological Treatment of the Hydrodynamical Equations
12.6. The Hydrodynamical Normal Modes
12.7. The Plasmadynamical Normal Modes
Appendix: Uniqueness Theorem for the Collisional Invariants
Chapter 13. Eigenvalues of the Kinetic Equations and the Theory of Transport Coefficients
13.1. Eigenvalues of the Linearized Kinetic Equation for a Homogeneous Gas
13.2. The "Normal" State of an Inhomogeneous Gas
13.3. Eigenvalues of the Linearized Kinetic Equation for an Inhomogeneous Gas
13.4. The Microscopic Expressions of the Transport Coefficients
13.5. Explicit Calculation of a Transport Coefficient
13.6. Eigenvalues of the Linearized Kinetic Equation for an Inhomogeneous Plasma
Chapter 14. Dynamics of Correlations
14.1. Time Evolution of the Classical Correlation Patterns
14.2. Classical Dynamics as a Dynamics of Correlations
14.3. Quantum Dynamics of Correlations
Chapter 15 Dynamics and Subdynamics of Ideal Systems
15.1. Solution of the Unperturbed Liouville Equation
15.2. The Resolvent Operator
15.3. Vacuum and Correlations: The Concept of Subdynamics
Chapter 16 Dynamics and Subdynamics of Interacting Systems
16.1. Formal Solution of the Liouville Equation
16.2. Program for a Kinetic Theory of Irreversibility
16.3. Further Transformation of the Resolvent Operator: The Irreducible Evolution Operator ε(z)—The Master Equation
16.4. Construction of the Operator Π
Appendix 1: Proof of the Relation Σ(t)= Π U(t)
Appendix 2: Proof of the Relation Π^2 = Π
Chapter 17 Subdynamics and Kinetic Theory
17.1. The Kinetic Component of the Correlations
17.2. The General Kinetic Equation
17.3. Time-Independent Functional Relations
17.4. Evolution of the Nonkinetic Component of the Distribution Vector
17.5. The Initial-Value Problem in Subdynamics
17.6. Spatially Homogeneous States
17.7. Equilibrium States
17.8. Nonequilibrium Stationary States
Chapter 18 The Evolution in Time of Weakly Coupled Gases
18.1. The Classical Kinetic Equation
18.2. The Classical Kinetic Correlations
18.3. The Spatially Homogeneous Classical Weakly Coupled Gas
18.4. The Inhomogeneous Classical Weakly Coupled Gas
18.5. The Nonkinetic Component of the Distribution Vector
18.6. The Quantum Kinetic Equation and Kinetic Correlations
18.7. The Spatially Homogeneous Quantum Weakly Coupled Gas
18.8. Properties of the Quantum Kinetic Equation
Chapter 19 Translation of the General Formalism into Explicit Equations
19.1. Reduction of the Kinetic Equation
19.2. The Diagram Representation of the Irreducible Evolution Operator
19.3. The Diagram Representation of the Kinetic Equation and of the Correlation Functions
Chapter 20 Special Kinetic Equations
20.1. Rearrangements of the Perturbation Expansion: Divergences
20.2. Dilute Gas of Strongly Interacting Particles
20.3. Two-Body Scattering Theory and the Boltzmann Equation
20.4. Kinetic Equations for Moderately Dense Gases
20.5. Classical Plasmas out of Equilibrium
20.6. Kinetic Equation for Classical Plasmas
20.7. Other Soluble Problems
Chapter 21 Dynamics of Fluctuations and of Correlations
21.1. Definition and Classification of Correlation Functions
21.2. The Green-Kubo Formulas for the Transport Coefficients
21.3. The Fluctuation-Dissipation Theorem
21.4. The Thermal Transport Coefficients
21.5. "Long Tails" in the Correlation Functions
21.6. Many-Times-Reduced Distribution Functions
21.7. Dynamics of Two-Time Distribution Functions
Chapter 22 Conclusion
Appendix: The Ergodic Problem
A.l. Trajectories and Integrals of the Motion
A.2. Two Harmonic Oscillators
A.3. The Kolmogorov-Arnold-Moser Theorem
A.4. Numerical Experiments on Simple Dynamical Systems
A.5. Measure in Phase Space
A.6. Ergodicity and Mixing: Sinai's Theorem
A.7. Ergodic Theory and Statistical Mechanics
Author Index
Subject Index

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