| Preface | p. vii |
| Notations and Fundamental Constants | p. xi |
| Basic Concepts | p. 1 |
| Introduction | p. 1 |
| Master Equation and Hypothesis of Equal á-priori Probability | p. 3 |
| Example of 3 Level Systems | p. 4 |
| Phase Space, Phase Point, Phase Trajectory | p. 4 |
| Statistical Distribution Function and Ergodic Hypothesis | p. 5 |
| Statistical Fluctuation and Statistical Independence | p. 7 |
| Statistical Fluctuation and Generalized Susceptibility | p. 11 |
| Generalized Ornstein-Zernicke Relation | p. 13 |
| Problems | p. 15 |
| Motion of Systems in Phase Space | p. 17 |
| Integral Invariants | p. 17 |
| Classical Liouville's Equation | p. 20 |
| Role of Energy | p. 22 |
| Quantum Mechanical Density Matrix | p. 22 |
| Quantum Liouville's Equation | p. 24 |
| Problems | p. 26 |
| States in Statistical Physics | p. 27 |
| Microscopic and Macroscopic States | p. 27 |
| Statistical Weight and Density of States | p. 28 |
| Examples: Non-interacting One- and N-Particle Systems and Spin-1/2 Particles | p. 29 |
| Entropy and Boltzmann's Principle | p. 31 |
| Boltzmann's H-Theorem | p. 34 |
| Problems | p. 35 |
| Statistical Ensembles | p. 37 |
| Introduction | p. 37 |
| Microcanonical Distribution Function | p. 37 |
| Canonical (Gibbs) Distribution Function | p. 39 |
| Thermodynamic Temperature and Distribution Function | p. 39 |
| Spin-1/2 Particles and Negative Temperature | p. 40 |
| Partition Function and Different Thermodynamic Functions | p. 41 |
| System of Linear Harmonic Oscillators in Canonical Ensemble | p. 42 |
| Energy Fluctuation in Canonical Ensemble and Equivalence of Canonical and Microcanonical Ensembles | p. 43 |
| Grandcanonical Distribution Function | p. 44 |
| Dependence of Thermodynamic Functions on Number of Particles | p. 44 |
| Chemical Potential and Distribution Function | p. 47 |
| Density Fluctuation in Grandcanonical Ensemble and Equivalence of Grandcanonical and Canonical Ensembles | p. 49 |
| Problems | p. 50 |
| Ideal Gas | p. 51 |
| Boltzmann Distribution | p. 51 |
| Partition Function, Free Energy and Equation of State | p. 52 |
| Specific Heat: Translational, Vibrational and Rotational Components | p. 55 |
| Degeneracy Temperature | p. 59 |
| Problems | p. 61 |
| Chemical Reaction Equilibrium | p. 63 |
| Conditions of Chemical Equilibrum | p. 63 |
| Law of Mass Action | p. 65 |
| Heat of Reaction and Direction of Reaction | p. 66 |
| Ionization Equilibrium | p. 68 |
| Saha Formula | p. 70 |
| Problems | p. 71 |
| Real Gas | p. 73 |
| Free Energy, Virial Equation of State | p. 73 |
| Second Virial Coefficient and Applicability of Virial Equation | p. 76 |
| Model Calculation and van-der-Waal's Equation of State | p. 78 |
| Joule-Thomson Expansion and Inversion Temperature | p. 80 |
| Problems | p. 83 |
| Strong Electrolytes | p. 85 |
| Debye-Hückel Approximation, Debye Length | p. 85 |
| Screened Coulomb Potential | p. 88 |
| Equation of State and Osmotic Pressure | p. 89 |
| Problems | p. 90 |
| Quantum Statistics | p. 91 |
| Bose and Fermi Distributions | p. 91 |
| Quantum Gases of Elementary Particles: Number Density and Chemical Potential, Energy Density, Equation of State | p. 94 |
| Black Body Radiation and Planck's Law | p. 98 |
| Lattice Specific Heat and Phonons | p. 100 |
| Degenerate Bose Gas, Bose Condensation | p. 103 |
| Liquid He and Superfluidity | p. 106 |
| Systematics of Liquid 4He | p. 106 |
| Landau's 2-Fluid Model | p. 111 |
| Systematics of Liquid 3He | p. 117 |
| Degenerate Fermi Gas, Degeneracy Pressure, Specific Heat | p. 118 |
| Magnetism of Free Fermions | p. 124 |
| Preamble | p. 124 |
| Landau Diamagnetism | p. 124 |
| Pauli Paramagnetism | p. 127 |
| Interacting Fermi System: Fermi Liquid Theory | p. 129 |
| Relativistic Degenerate Fermi Gas | p. 133 |
| Problems | p. 136 |
| Bose-Einstein Condensate | p. 139 |
| Introduction | p. 139 |
| Trapping of Atoms | p. 140 |
| Cooling of Atoms | p. 142 |
| Problems | p. 145 |
| Statistical Astrophysics | p. 147 |
| Introduction | p. 147 |
| Stars: Stability and Evolution | p. 148 |
| High Temperature Dense Matter | p. 152 |
| Neutron Stars and Black Holes | p. 154 |
| Problems | p. 156 |
| Phase Transitions | p. 157 |
| Systematics of Phase Transitions | p. 157 |
| Ehrenfest's Classification of Phase Transitions | p. 159 |
| Order Parameter, Continuous and Discontinuous Transitions | p. 160 |
| Landau's Theory of Continuous Phase Transitions | p. 163 |
| Continuity of Entropy and Discontinuity of Specific Heat | p. 165 |
| Generalized Susceptibility | p. 167 |
| Critical Exponents and Fluctuations of Order Parameter | p. 170 |
| Ising Model | p. 173 |
| Zero-Field 1-Dimensional Case | p. 175 |
| Non-Zero-Field 1-Dimensional Case | p. 175 |
| Multi-Dimensional Case | p. 177 |
| 2-Dimensional Ising System | p. 178 |
| Problems | p. 181 |
| Irreversible Processes | p. 183 |
| Introduction | p. 183 |
| Linear Response Theory (Kubo Formalism) | p. 184 |
| Mechanical Process | p. 184 |
| Thermal Process | p. 189 |
| Symmetry Relations | p. 191 |
| Fluctuation-Dissipation Theorem | p. 192 |
| Problems | p. 196 |
| Mathematical Appendix | p. 197 |
| Beta and Gamma Functions | p. 197 |
| Dirac Delta Function (Distribution) | p. 198 |
| Functional Derivative | p. 200 |
| Mathematical Identities | p. 201 |
| Multiple Summation | p. 202 |
| Pauli Matrices | p. 203 |
| Probability Theory | p. 203 |
| Elementary Results of Probability Theory | p. 203 |
| Statistical Distributions | p. 204 |
| Central Limit Theorem | p. 207 |
| Quantum Mechanics, A Retrospect | p. 209 |
| Riemann, Bernoulli and Fourier | p. 210 |
| Riemann's ¿-Function | p. 210 |
| Bernoulli Numbers and Polynomials | p. 211 |
| Fourier Series | p. 212 |
| Integrals of Quantum Statistics | p. 214 |
| Sanskrit Transliteration | p. 216 |
| Stirling's Theorem | p. 217 |
| Summation and Integration | p. 219 |
| Volume of an N-Dimensional Sphere | p. 220 |
| Bibliography | p. 223 |
| Index | p. 225 |
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