Non-Equilibrium Statistical MechanicsIlya 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. |
Contents
| 1 | |
The Liouville Equation | 13 |
Anharmonic Solids | 36 |
Brownian Motion | 67 |
Weakly Coupled Gases | 86 |
Approach to Equilibrium in Weakly Coupled Gases | 106 |
Scattering Theory and ShortRange Forces | 113 |
The Diagram Representation | 138 |
General Kinetic Equations | 226 |
General HTheorem | 244 |
Quantum Mechanics | 257 |
Irreversibility and Invariants of Motion | 265 |
Laguerre Functions and Bessel Functions | 279 |
Derivation of the Master Equation by TimeIndependent | 291 |
General Theory of Anharmonic Oscillators | 297 |
Bibliography | 308 |
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Common terms and phrases
action-angle variables analytic approach to equilibrium arbitrary articulation point asymptotic Balescu Boltzmann equation Brownian motion Chapter classical collision condition contribution coordinates correlations corresponding degrees of freedom density dependence derived destruction region diagonal fragments diagrams of Fig duration eigenfunctions energy equilibrium statistical mechanics evolution example expression factor finite Fokker-Planck equation formula Fourier coefficients Fourier transform H-theorem Hamiltonian hydrodynamic inhomogeneity integral interaction introduce invariants k₁ kk'k Laguerre polynomials Let us consider Liouville equation Liouville operator master equation matrix element molecular molecular chaos molecules momenta N-body problem normal modes notation obtain oscillators P₁ particles phase space Po(t Prigogine problem propagation quantum mechanics reduced distribution functions relation Résibois scattering singularity situations solution summation theorem theory tint tion transition unperturbed valid values vanishes variables velocity distribution function vertex wave vectors weakly coupled gases weakly coupled systems α α ΣΣ