Non equilibrium statistical mechanics 1st edition by Prigogine Ilya 0486815552 9780486815558

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ISBN-10 :  0486815552 

ISBN-13 :  9780486815558

Author:  Prigogine Ilya 

Ilya Prigogine won the 1977 Nobel Prize in Chemistry for his contributions to non-equilibrium thermodynamics. This groundbreaking 1962 monograph, written for researchers and graduate students in this field, was his first book-length contribution to this subject. Suitable for advanced undergraduates and graduate students in physics and chemistry, the treatment begins with examinations of the Liouville equation, anharmonic solids, and Brownian motion. Subsequent chapters explore weakly coupled gases, scattering theory and short-range forces, distribution functions and their diagrammatic representation, the time dependence of diagrams, the approach to equilibrium in ionized gases, and statistical hydrodynamics. Additional topics include general kinetic equations, general H-theorem, quantum mechanics, and irreversibility and invariants of motion. Appendices, a bibliography, list of symbols, and an index conclude the text.

Non equilibrium statistical mechanics 1st Table of contents:

1. The Liouville Equation
1. The Phase Space of a Mechanical System
2. Representative Ensembles
3. The Liouville Equation
4. Formal Solution of the Liouville Equation
5. Non-Interacting Particles
6. Action-Angle Variables
7. Liouville’s Theorem in Action-Angle Variables
8. Liouville’s Equation in Interaction Representation
9. Example
10. Discussion of the Interaction Representation
11. Time-Dependent and Time-Independent Perturbation Theory
2. Anharmonic Solids
1. Hamiltonian
2. The Liouville Operator
3. Formal Solution for the Energy Distribution Function
4. Diagram Technique
5. Second-Order Contributions
6. Fourth-Order Contributions
7. Master Equation
8. H-Theorem
9. Fokker-Planck Equation and Master Equation
3. Brownian Motion
1. Basic Equations
2. Approach to Equilibrium
3. Statistical Theory of Brownian Motion
4. Evolution of the Fourier Components
5. Brownian Motion in Displacement and Velocity
6. Comparison with the Phenomenological Theory of Brownian Motion
4. Weakly Coupled Gases
1. Liouville Operator
2. Master Equation for Weakly Coupled Gases—Diagrams
3. Boltzmann Equation and Molecular Chaos
4. Explicit Form of the Boltzmann Equation
5. Brownian Motion
6. Fokker-Planck Equation and Dynamical Friction
7. Electrostatic Interactions — The Divergence Problem
5. Approach to Equilibrium in Weakly Coupled Gases
1. Introduction
2. H-Theorem
3. Disappearance of Inhomogeneities
4. Discussion
6. Scattering Theory and Short-Range Forces
1. Two-Body Scattering Theory
2. Propagators
3. Scattering in Phase Space
4. Equilibrium Distribution and Scattering Theory
5. iV-Body Problem in the Limit of Low Concentrations
6. Master Equation in the Limit of Low Concentrations
7. Scattering Theory and the N-Body Problem
7. Distribution Functions: The Diagram Representation
1. Distribution Functions
2. Fourier Expansion and Distribution Functions
3. Singularities in the Fourier Expansion
4. Cluster Expansion of the Distribution Functions
5. Physical Meaning of the Fourier Coefficients
6. Diagrams
7. Concentration Dependence of Diagrams
8. Reduced Distribution Functions and Diagrams
8. The Time Dependence of Diagrams
1. Effect of H0—Wave Packets
2. Duration of a Collision
3. Resolvent Method
4. Analytic Behavior of the Resolvent
5. Diagonal Fragments
6. Free Propagation and Scattering
7. Destruction of Correlations
8. Creation of Correlations
9. Propagation of Correlations
10. General Remarks about the Time Dependence of Diagrams
11. Velocity Distribution in Weakly Coupled or Dilute Systems
12. The Thermodynamic Case
13. Dynamics of Correlations and Time Dependence
9. Approach to Equilibrium in Ionized Gases
1. Choice of Diagrams
2. Summation of Rings
3. Solution of the Integral Equation
4. Discussion of the Transport Equation
10. Statistical Hydrodynamics
1. Introduction
2. Transport Equation in the Limit of Large Free Paths
3. Factorization Theorems for Fourier Coefficients
4. Time Scales and Diagrams
5. Transport Equation in the Hydrodynamic Case — the Boltzmann Equation
6. Discussion of the Approach to Equilibrium in Inhomogeneous Systems
11. General Kinetic Equations
1. Evolution of the Velocity Distribution
2. Markowian Form of the Evolution Equation for the Velocity Distribution
3. Evolution of Correlations
4. Hydrodynamic Situations
5. Bogoliubov’s Theory
6. Stationary Non-Equilibrium States — Kinetic Equations and Time Scales
12. General H-Theorem
1. Introduction
2. Approach to Equilibrium of the Velocity Distribution Function
3. Approach to Equilibrium of the Correlations
4. Articulation Points and Principle of Detailed Balance
5. Two-Particle Correlation Function
6. Mechanism of Irreversibility
13. Quantum Mechanics
1. Quantum Mechanical Density Matrix
2. Quantum Mechanical Liouville Equation in Interaction Representation
3. Wave Vector Conservation
4. Pauli Equation
14. Irreversibility and Invariants of Motion
1. The condition of Dissipativity
2. Dissipativity and Poincaré’s Theorem
3. Analytic Invariants with singular Fourier Transforms
4. Approach to Equilibrium and Invariants

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