Statistical Mechanics

Statistical Mechanics

3rd Edition - February 28, 2011

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  • Author: Paul Beale
  • eBook ISBN: 9780123821898

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Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. This edition includes new topics such as BoseEinstein condensation and degenerate Fermi gas behavior in ultracold atomic gases and chemical equilibrium. It also explains the correlation functions and scattering; fluctuationdissipation theorem and the dynamical structure factor; phase equilibrium and the Clausius-Clapeyron equation; and exact solutions of one-dimensional fluid models and two-dimensional Ising model on a finite lattice. New topics can be found in the appendices, including finite-size scaling behavior of Bose-Einstein condensates, a summary of thermodynamic assemblies and associated statistical ensembles, and pseudorandom number generators. Other chapters are dedicated to two new topics, the thermodynamics of the early universe and the Monte Carlo and molecular dynamics simulations. This book is invaluable to students and practitioners interested in statistical mechanics and physics.

Key Features

  • 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
  • Chemical equilibrium
  • Exact solution of the two-dimensional Ising model for finite systems
  • Degenerate atomic Fermi gases
  • Exact solutions of one-dimensional fluid models
  • Interactions in ultracold Bose and Fermi gases
  • Brownian motion of anisotropic particles and harmonic oscillators


Graduate and Advanced Undergraduate Students in Physics. Researchers in the field of Statisical Physics

Table of Contents

  • Chapter 1: The Statistical Basis of Thermodynamics

    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


    Chapter 2: Elements of Ensemble Theory

    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


    Chapter 3: The Canonical Ensemble

    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


    Chapter 4: The Grand Canonical Ensemble

    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


    Chapter 5: Formulation of Quantum Statistics

    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


    Chapter 6: The Theory of Simple Gases

    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


    Chapter 7: Ideal Bose Systems

    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


    Chapter 8: Ideal Fermi Systems

    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


    Chapter 9: Thermodynamics of the Early Universe

    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


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

    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


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

    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 theory21

    11.9 Condensation in Fermi systems


    Chapter 12: Phase Transitions: Criticality, Universality, and Scaling

    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


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

    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


    Chapter 14: Phase Transitions: The Renormalization Group Approach

    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


    Chapter 15: Fluctuations and Nonequilibrium Statistical Mechanics

    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


    Chapter 16: Computer Simulations

    16.1 Introduction and statistics

    16.2 Monte Carlo simulations

    16.3 Molecular dynamics

    16.4 Particle simulations

    16.5 Computer simulation caveats


Product details

  • No. of pages: 744
  • Language: English
  • Copyright: © Academic Press 2011
  • Published: February 28, 2011
  • Imprint: Academic Press
  • eBook ISBN: 9780123821898

About the Author

Paul Beale

Paul D. Beale is a Professor of Physics at the University of Colorado Boulder. He earned a B.S. in Physics with Highest Honors at the University of North Carolina Chapel Hill in 1977, and Ph.D. in Physics from Cornell University in 1982. He served as a postdoctoral research associate at the Department of Theoretical Physics at Oxford University from 1982-1984. He joined the faculty of the University of Colorado Boulder in 1984 as an assistant professor, was promoted to associate professor in 1991, and professor in 1997. He served as the Chair of the Department of Physics from 2008-2016. He also served as Associate Dean for Natural Sciences in the College of Arts and Sciences, and Director of the Honors Program. He is currently Director of the Buffalo Bicycle Classic, the largest scholarship fundraising event in the State of Colorado. Beale is a theoretical physicist specializing in statistical mechanics, with emphasis on phase transitions and critical phenomena. His work includes renormalization group methods, finite-size scaling in spin models, fracture modes in random materials, dielectric breakdown in metal-loaded dielectrics, ferroelectric switching dynamics, exact solutions of the finite two-dimensional Ising model, solid-liquid phase transitions of molecular systems, and ordering in layers of molecular dipoles. His current interests include scalable parallel pseudorandom number generators, and interfacing quantum randomness with cryptographically secure pseudorandom number generators. He is coauthor with Raj Pathria of the third and fourth editions of the graduate physics textbook Statistical Mechanics. The Boulder Faculty Assembly has honored him with the Excellence in Teaching and Pedagogy Award, and the Excellence in Service and Leadership Award. Beale is a private pilot and an avid cyclist. He is married to Erika Gulyas, and has two children: Matthew and Melanie.

Affiliations and Expertise

Professor of Physics, University of Colorado, Boulder, USA

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  • DanielWiley Mon Apr 08 2019

    Statistical Mechanics

    A terrific introductory textbook for graduate students in physics. The option to include electronic copies of the text with a hardcover purchase is very helpful and convenient.