Fundamentals of Statistical Mechanics

The following sections are included:

• Preface

• Second Preface

• Contents

The mechanics of macroscopic systems with many degrees of freedom does not usually allow a rigorous treatment, since the equations of motion are prohibitively difficult to solve in all but a few special cases. Even in these cases, however, one is confronted with the more fundamental difficulty that the information available in practice is far from being sufficient to select the particular solution that best describes a given individual system. In fact, the actual observations normally furnish no more than a small set of macroscopic data, whereas the knowledge of all the many dynamical variables would be required to fully determine the state of the system. With the underlying mechanical process thus largely unspecified, one can account for the observed properties only by resorting to statistical methods…

The following sections are included:

• Hamilton's Equations

• Phase Space

• Liouville's Theorem

The following sections are included:

• Distribution Function and Probability Density

• Mean Values
  • Additive Quantities

• Time Dependence of the Phase Density

The following sections are included:

• Stationary Mean Values
  • Conditions of Equilibrium

• Constancy of the Distribution Function

• The Canonical Distribution

• Thermodynamic Functions

• The Partition Function

• The Statistical Significance of Entropy

The following sections are included:

• Ideal Monatomic Gases
  • Energy
  • Heat Capacity
  • Entropy
  • Free Energy
  • Distribution in the μ-Space

• The Virial Theorem

• The Equipartition Theorem

• Examples
  • Mean Kinetic Energy
  • Diatomic Moleculas
    • Rigid Rotation
    • Vibrations
  • Solids
    • Normal Coordinates
    • Linear Chain
    • Periodic Boundary Conditions
    • Three-Dimensional Solid
  • Black-Body Radiation

• Magnetism

The following sections are included:

• Basic Elements of Quantum Mechanics

• The Density Matrix

• The Statistical Ensemble

• Time Dependence of the Density Matrix

• Thermal Equilibrium

• The Canonical Distribution

• Thermodynamic Functions and the Partition Function
  • The Nernst Heat Theorem

The followingn sections are included:

• Ideal Monatomic Gases

• Mean Energy of Harmonic Oscillator

• Examples
  • Diatomic Molecules
  • Specific Heat of Solids
    • The Debye Approximation
  • Black-Body Radiation
  • Magnetism
    • Weiss Theory of Ferromagnetism
  • Transition from Quantum to Classical Statistical Mechanics

• Identical Particles

• The Grand Canonical Ensemble

• Fermi Statistics

• Bose Statistics

The following sections are included:

• Appendix A: Canonical Transformations and Poisson Brackets

• Appendix B: General Proof of Liouville's Theorem

• Appendix C: Molecular Distributions

• Appendix D: Some Properties of Fourier Series

• Appendix E: Basic Texts and Monographs

• Problems

• Index