Front Cover -- Statistical Mechanics -- Copyright Page -- Contents -- Preface to the Second Edition -- Preface to the First Edition -- Historical Introduction -- Notes -- 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 -- Problems -- Notes -- 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 -- Problems -- Notes -- 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 -- Problems -- Notes -- 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 -- Problems -- Notes.

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 -- Problems -- Notes -- 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 -- Problems -- Notes -- Chapter 7. Ideal Bose Systems -- 7.1. Thermodynamic behavior of an ideal Bose gas -- 7.2. Thermodynamics of the black-body radiation -- 7.3. The field of sound waves -- 7.4. Inertial density of the sound field -- 7.5. Elementary excitations in liquid helium II -- Problems -- Notes -- 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. Statistical equilibrium of white dwarf stars -- 8.5. Statistical model of the atom -- Problems -- Notes -- Chapter 9. Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions -- 9.1. Cluster expansion for a classical gas -- 9.2. Virial expansion of the equation of state -- 9.3. Evaluation of the virial coefficients -- 9.4. General remarks on cluster expansions -- 9.5. Exact treatment of the second virial coefficient -- 9.6. Cluster expansion for a quantum-mechanical system -- Problems -- Notes -- Chapter 10. Statistical Mechanics of Interacting Systems: The Method of Quantized Fields -- 10.1. The formalism of second quantization -- 10.2. Low-temperature behavior of an imperfect Bose gas.

10.3. Low-lying states of an imperfect Bose gas -- 10.4. Energy spectrum of a Bose liquid -- 10.5. States with quantized circulation -- 10.6. Quantized vortex rings and the breakdown of superfluidity -- 10.7. Low-lying states of an imperfect Fermi gas -- 10.8. Energy spectrum of a Fermi liquid: Landau's phenomenological theory -- Problems -- Notes -- Chapter 11. Phase Transitions: Criticality, Universality and Scaling -- 11.1. General remarks on the problem of condensation -- 11.2. Condensation of a van der Waals gas -- 11.3. A dynamical model of phase transitions -- 11.4. The lattice gas and the binary alloy -- 11.5. Ising model in the zeroth approximation -- 11.6. Ising model in the first approximation -- 11.7. The critical exponents -- 11.8. Thermodynamic inequalities -- 11.9. Landau's phenomenological theory -- 11.10. Scaling hypothesis for thermodynamic functions -- 11.11. The role of correlations and fluctuations -- 11.12. The critical exponents v and η -- 11.13. A final look at the mean, field theory -- Problems -- Notes -- Chapter 12. Phase Transitions: Exact (or Almost Exact) Results for the Various Models -- 12.1. The Ising model in one dimension -- 12.2. The n-vector models in one dimension -- 12.3. The Ising model in two dimensions -- 12.4. The spherical model in arbitrary dimensions -- 12.5. The ideal Bose gas in arbitrary dimensions -- 12.6. Other models -- Problems -- Notes -- Chapter 13. Phase Transitions: The Renormalization Group Approach -- 13.1. The conceptual basis of scaling -- 13.2. Some simple examples of renormalization -- 13.3. The renormalization group: general formulation -- 13.4. Applications of the renormalization group -- 13.5. Finite-size scaling -- Problems -- Notes -- Chapter 14. Fluctuations -- 14.1. Thermodynamic fluctuations -- 14.2. Spatial correlations in a fluid.

14.3. The Einstein-Smoluchowski theory of the Brownian motion -- 14.4. The Langevin theory of the Brownian motion -- 14.5. Approach to equilibrium: the Fokker- Planck equation -- 14.6. Spectral analysis of fluctuations: the Wiener- Khintchine theorem -- 14.7. The fluctuation- dissipation theorem -- 14.8. The Onsager relations -- Problems -- Notes -- Appendixes -- 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. On Watson functions -- Notes -- Bibliography -- Index.