preface to the third edition preface to the second edition preface to the first edition historical introduction 1. the statistical basis of thermodynamics 1.1. the macroscopic and the microscopic states 1.2. contact between statistics and thermodynamics:physicalsignificance of the number (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 2. elements of ensemble theory 2.1. phase space of a classical system 2.2. liouville's theorem and its consequences 2.3. the microcanordcal ensemble 2.4. examples 2.5. quantum states and the phase space problems 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 quantitiesin the canonical ensemble 3.4. alternative expressions for the partition function 3.5. the classical systems 3.6. energy fluctuations in the canonical ensemble:correspondencewith 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:negativetemperatures problems 4. the grand canonical ensemble 4.1. equilibrium between a system and a particle-energyreservoir 4.2. a system in the grand canonical ensemble 4.3. physical significance of the various statisticalquantities 4.4. examples 4.5. density and energy fluctuations in the grand canonicalensemble: correspondence with other ensembles 4.6. thermodynamic phase diagrams 4.7. phase equilibrium and the clausius-clapeyron equation problems 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 offree particles problems 6. the theory of simple gases 6.1. an ideal gas in a quantum-mechanical microcanonicalensemble 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 internalmotion 6.6. chemical equilibrium problems 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 problems 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 problems 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 problems 10. statistical mechanics of interacting systems:the method ofcluster 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 problems 11. statistical mechanics of interacting systems:the method ofquantized 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 ofsuperfluidity 11.7. low-lying states of an imperfect fermi gas 11.8. energy spectrum of a fermi liquid: landau's phenomenologicaltheory 11.9. condensation in fermi systems problems 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 v and 12.13. a final look at the mean field theory problems 13. phase transitions: exact (or almost exact) results for variousmodels 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 problems 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 problems 15. fluctuations and nonequilibrium statistical mechanics 15.1. equilibrium thermodynamic fluctuations 15.2. the einstein-smoluchowski theory of the brownianmotion 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-khintchinetheorem 15.6. the fluctuation-dissipation theorem 15.7. the onsager relations problems 16. computer simulations 16.1. introductionand statistics 16.2. monte carlo simulations 16.3. molecular dynamics 16.5. computer simulation caveats problems appendices a. influence of boundary conditions on the distribution of quantumstates b. certain mathematical functions c. \volume\ and \surface area\ of an n-dimensional sphere ofradius r d. on bose-einstein functionse. on fermi-dirac functions f. a rigorous analysis of the ideal bose gas and the onset ofbose-einstein condensation g. on watson functions h. thermodynamic relationships i. pseudorandom numbers bibliography index
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