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Statistical Mechanics 4th edition by Pathria, Beale ISBN 0081026935 9780081026939

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ISBN 10: 0081026935
ISBN 13: 9780081026939
Author:  Pathria, Beale

Statistical Mechanics, Fourth Edition, explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. This valuable textbook introduces the reader to the historical context of the subject before delving deeper into chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. In the latest revision, the book’s authors have updated the content throughout, including new coverage on biophysical applications, updated exercises, and computer simulations. This updated edition will be an indispensable to students and researchers of statistical mechanics, thermodynamics, and physics.

  • Retains the valuable organization and trusted coverage of previous market-leading editions
  • Includes new coverage on biophysical applications and computer simulations
  • Offers Mathematica files for student use and a secure solutions manual for qualified instructors
  • Covers Bose-Einstein condensation in atomic gases, Thermodynamics of the early universe, Computer simulations: Monte Carlo and molecular dynamics, Correlation functions and scattering, Fluctuation-dissipation theorem and the dynamical structure factor, and much more

Statistical Mechanics 4th Table of contents:

1: The Statistical Basis of Thermodynamics

  • Abstract
  • 1.1. The Macroscopic and the Microscopic States
  • 1.2. Contact Between Statistics and Thermodynamics: Physical Significance of the Number Ω(N, V, E)
  • 1.3. Further Contact Between Statistics and Thermodynamics
  • 1.4. The Classical Ideal Gas
  • 1.5. The Entropy of Mixing and the Gibbs Paradox
  • 1.6. The “Correct” Enumeration of the Microstates
  • Problems
  • Bibliography

2: Elements of Ensemble Theory

  • Abstract
  • 2.1. Phase Space of a Classical System
  • 2.2. Liouville’s Theorem and Its Consequences
  • 2.3. The Microcanonical Ensemble
  • 2.4. Examples
  • 2.5. Quantum States and the Phase Space
  • Problems
  • Bibliography

3: The Canonical Ensemble

  • Abstract
  • 3.1. Equilibrium Between a System and a Heat Reservoir
  • 3.2. A System in the Canonical Ensemble
  • 3.3. Physical Significance of the Various Statistical Quantities in the Canonical Ensemble
  • 3.4. Alternative Expressions for the Partition Function
  • 3.5. The Classical Systems
  • 3.6. Energy Fluctuations in the Canonical Ensemble: Correspondence with the Microcanonical Ensemble
  • 3.7. Two Theorems – the “Equipartition” and the “Virial”
  • 3.8. A System of Harmonic Oscillators
  • 3.9. The Statistics of Paramagnetism
  • 3.10. Thermodynamics of Magnetic Systems: Negative Temperatures
  • Problems
  • Bibliography

4: The Grand Canonical Ensemble

  • Abstract
  • 4.1. Equilibrium Between a System and a Particle–Energy Reservoir
  • 4.2. A System in the Grand Canonical Ensemble
  • 4.3. Physical Significance of the Various Statistical Quantities
  • 4.4. Examples
  • 4.5. Density and Energy Fluctuations in the Grand Canonical Ensemble: Correspondence with Other Ensembles
  • 4.6. Thermodynamic Phase Diagrams
  • 4.7. Phase Equilibrium and the Clausius–Clapeyron Equation
  • Problems
  • Bibliography

5: Formulation of Quantum Statistics

  • Abstract
  • 5.1. Quantum-Mechanical Ensemble Theory: The Density Matrix
  • 5.2. Statistics of the Various Ensembles
  • 5.3. Examples
  • 5.4. Systems Composed of Indistinguishable Particles
  • 5.5. The Density Matrix and the Partition Function of a System of Free Particles
  • 5.6. Eigenstate Thermalization Hypothesis
  • Problems
  • Bibliography

6: The Theory of Simple Gases

  • Abstract
  • 6.1. An Ideal Gas in a Quantum-Mechanical Microcanonical Ensemble
  • 6.2. An Ideal Gas in Other Quantum-Mechanical Ensembles
  • 6.3. Statistics of the Occupation Numbers
  • 6.4. Kinetic Considerations
  • 6.5. Gaseous Systems Composed of Molecules with Internal Motion
  • 6.6. Chemical Equilibrium
  • Problems
  • Bibliography

7: Ideal Bose Systems

  • Abstract
  • 7.1. Thermodynamic Behavior of an Ideal Bose Gas
  • 7.2. Bose–Einstein Condensation in Ultracold Atomic Gases
  • 7.3. Thermodynamics of the Blackbody Radiation
  • 7.4. The Field of Sound Waves
  • 7.5. Inertial Density of the Sound Field
  • 7.6. Elementary Excitations in Liquid Helium II
  • Problems
  • Bibliography

8: Ideal Fermi Systems

  • Abstract
  • 8.1. Thermodynamic Behavior of an Ideal Fermi Gas
  • 8.2. Magnetic Behavior of an Ideal Fermi Gas
  • 8.3. The Electron Gas in Metals
  • 8.4. Ultracold Atomic Fermi Gases
  • 8.5. Statistical Equilibrium of White Dwarf Stars
  • 8.6. Statistical Model of the Atom
  • Problems
  • Bibliography

9: Thermodynamics of the Early Universe

  • Abstract
  • 9.1. Observational Evidence of the Big Bang
  • 9.2. Evolution of the Temperature of the Universe
  • 9.3. Relativistic Electrons, Positrons, and Neutrinos
  • 9.4. Neutron Fraction
  • 9.5. Annihilation of the Positrons and Electrons
  • 9.6. Neutrino Temperature
  • 9.7. Primordial Nucleosynthesis
  • 9.8. Recombination
  • 9.9. Epilogue
  • Problems
  • Bibliography

10: Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions

  • Abstract
  • 10.1. Cluster Expansion for a Classical Gas
  • 10.2. Virial Expansion of the Equation of State
  • 10.3. Evaluation of the Virial Coefficients
  • 10.4. General Remarks on Cluster Expansions
  • 10.5. Exact Treatment of the Second Virial Coefficient
  • 10.6. Cluster Expansion for a Quantum-Mechanical System
  • 10.7. Correlations and Scattering
  • Problems
  • Bibliography

11: Statistical Mechanics of Interacting Systems: The Method of Quantized Fields

  • Abstract
  • 11.1. The Formalism of Second Quantization
  • 11.2. Low-Temperature Behavior of an Imperfect Bose Gas
  • 11.3. Low-Lying States of an Imperfect Bose Gas
  • 11.4. Energy Spectrum of a Bose Liquid
  • 11.5. States with Quantized Circulation
  • 11.6. Quantized Vortex Rings and the Breakdown of Superfluidity
  • 11.7. Low-Lying States of an Imperfect Fermi Gas
  • 11.8. Energy Spectrum of a Fermi Liquid: Landau’s Phenomenological Theory
  • 11.9. Condensation in Fermi Systems
  • Problems
  • Bibliography

12: Phase Transitions: Criticality, Universality, and Scaling

  • Abstract
  • 12.1. General Remarks on the Problem of Condensation
  • 12.2. Condensation of a Van der Waals Gas
  • 12.3. A Dynamical Model of Phase Transitions
  • 12.4. The Lattice Gas and the Binary Alloy
  • 12.5. Ising Model in the Zeroth Approximation
  • 12.6. Ising Model in the First Approximation
  • 12.7. The Critical Exponents
  • 12.8. Thermodynamic Inequalities
  • 12.9. Landau’s Phenomenological Theory
  • 12.10. Scaling Hypothesis for Thermodynamic Functions
  • 12.11. The Role of Correlations and Fluctuations
  • 12.12. The Critical Exponents ν and η
  • 12.13. A Final Look at the Mean Field Theory
  • Problems
  • Bibliography

13: Phase Transitions: Exact (or Almost Exact) Results for Various Models

  • Abstract
  • 13.1. One-Dimensional Fluid Models
  • 13.2. The Ising Model in One Dimension
  • 13.3. The n-Vector Models in One Dimension
  • 13.4. The Ising Model in Two Dimensions
  • 13.5. The Spherical Model in Arbitrary Dimensions
  • 13.6. The Ideal Bose Gas in Arbitrary Dimensions
  • 13.7. Other Models
  • Problems
  • Bibliography

14: Phase Transitions: The Renormalization Group Approach

  • Abstract
  • 14.1. The Conceptual Basis of Scaling
  • 14.2. Some Simple Examples of Renormalization
  • 14.3. The Renormalization Group: General Formulation
  • 14.4. Applications of the Renormalization Group
  • 14.5. Finite-Size Scaling
  • Problems
  • Bibliography

15: Fluctuations and Nonequilibrium Statistical Mechanics

  • Abstract
  • 15.1. Equilibrium Thermodynamic Fluctuations
  • 15.2. The Einstein–Smoluchowski Theory of the Brownian Motion
  • 15.3. The Langevin Theory of the Brownian Motion
  • 15.4. Approach to Equilibrium: The Fokker–Planck Equation
  • 15.5. Spectral Analysis of Fluctuations: The Wiener–Khintchine Theorem
  • 15.6. The Fluctuation–Dissipation Theorem
  • 15.7. The Onsager Relations
  • 15.8. Exact Equilibrium Free Energy Differences from Nonequilibrium Measurements
  • Problems
  • Bibliography

16: Computer Simulations

  • Abstract
  • 16.1. Introduction and Statistics
  • 16.2. Monte Carlo Simulations
  • 16.3. Molecular Dynamics
  • 16.4. Particle Simulations
  • 16.5. Computer Simulation Caveats
  • Problems
  • Bibliography

Appendices

  • A. Influence of Boundary Conditions on the Distribution of Quantum States
  • B. Certain Mathematical Functions
  • C. “Volume” and “Surface Area” of an n-Dimensional Sphere of Radius R
  • D. On Bose–Einstein Functions
  • E. On Fermi–Dirac Functions
  • F. A Rigorous Analysis of the Ideal Bose Gas and the Onset of Bose–Einstein Condensation
  • G. On Watson Functions
  • H. Thermodynamic Relationships
  • I. Pseudorandom Numbers

Bibliography
Index

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