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Statistical Physics of Particles

Book Description

Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. 1.Thermodynamics
    1. 1.1 Introduction
    2. 1.2 The zeroth law
    3. 1.3 The first law
    4. 1.4 The second law
    5. 1.5 Carnot engines
    6. 1.6 Entropy
    7. 1.7 Approach to equilibrium and thermodynamic potentials
    8. 1.8 Useful mathematical results
    9. 1.9 Stability conditions
    10. 1.10 The third law
    11. Problems
  8. 2. Probability
    1. 2.1 General definitions
    2. 2.2 One random variable
    3. 2.3 Some important probability distributions
    4. 2.4 Many random variables
    5. 2.5 Sums of random variables and the central limit theorem
    6. 2.6 Rules for large numbers
    7. 2.7 Information, entropy, and estimation
    8. Problems
  9. 3. Kinetic theory of gases
    1. 3.1 General definitions
    2. 3.2 Liouville’s theorem
    3. 3.3 The Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy
    4. 3.4 The Boltzmann equation
    5. 3.5 The H-theorem and irreversibility
    6. 3.6 Equilibrium properties
    7. 3.7 Conservation laws
    8. 3.8 Zeroth-order hydrodynamics
    9. 3.9 First-order hydrodynamics
    10. Problems
  10. 4. Classical statistical mechanics
    1. 4.1 General definitions
    2. 4.2 The microcanonical ensemble
    3. 4.3 Two-level systems
    4. 4.4 The ideal gas
    5. 4.5 Mixing entropy and the Gibbs paradox
    6. 4.6 The canonical ensemble
    7. 4.7 Canonical examples
    8. 4.8 The Gibbs canonical ensemble
    9. 4.9 The grand canonical ensemble
    10. Problems
  11. 5. Interacting particles
    1. 5.1 The cumulant expansion
    2. 5.2 The cluster expansion
    3. 5.3 The second virial coefficient and van der Waals equation
    4. 5.4 Breakdown of the van der Waals equation
    5. 5.5 Mean-field theory of condensation
    6. 5.6 Variational methods
    7. 5.7 Corresponding states
    8. 5.8 Critical point behavior
    9. Problems
  12. 6. Quantum statistical mechanics
    1. 6.1 Dilute polyatomic gases
    2. 6.2 Vibrations of a solid
    3. 6.3 Black-body radiation
    4. 6.4 Quantum microstates
    5. 6.5 Quantum macrostates
    6. Problems
  13. 7. Ideal quantum gases
    1. 7.1 Hilbert space of identical particles
    2. 7.2 Canonical formulation
    3. 7.3 Grand canonical formulation
    4. 7.4 Non-relativistic gas
    5. 7.5 The degenerate fermi gas
    6. 7.6 The degenerate bose gas
    7. 7.7 Superfluid He4
    8. Problems
  14. Solutions to selected problems
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
  15. Index