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Foreword Preface I Thermodynamics 1. Equilibrium and State Quantities Introduction Systems, phases and state quantities Equilibrium and temperature the zeroth law of thermodynamics Kinetic theory of the ideal gas Pressure, work and chemical potential Heat and heat capacity The equation of state for a real gas Specific heat Changes of state--reversible and irreversible processes Exact and inexact differentials, line integrals 2. The Laws of Thermodynamics The first law Carnot's process and entropy Entropy and the second law Insertion: Microscopic interpretation of entropy and of the second law Global and local equilibrium Thermodynamic engines Euler's equation and the Gibbs-Duhem relation 3. Phase Transitions and Chemical Reactions Gibbs' Phase Rule Phase equilibrium and the Maxwell construction The law of mass action Application of the laws of thermodynamics 4. Thermodynamic Potentials The principle of maximum entropy Entropy and energy as thermodynamic potentials The Legendre transformation The free energy The cnthalpy The free enthalpy The grand potential The transformation of all variables The Maxwell relations Jacobi transformations Thermodynamic stability II Statistical Mechanics 5. Number of Microstates ¦¸ and Entropy S Foundations Phase space Statistical definition of entropy Gibbs' paradox Pseudo quantum mechanical counting of ¦¸ 6. Ensemble Theory and Microcanonical Ensemble Phase-space density, ergodic hypothesis Liouville's theorem The microcanonical ensemble Entropy as an ensemble average The uncertainty function 7. The Canonical Ensemble General foundation of the Gibbs correction factor Systems of noninteracting particles Calculation of observables as ensemble averages Connection between microcanonical and canonical ensembles Fluctuations Vh-ial theorem and equipartition theorem For better understanding: canonical ensemble as the mean value of all possible distributions 8. Applications of Boltzmann Statistics Quantum Systems in Boltzmann Statistics Paramagnetism Negative temperatures in two-level systems Gases with internal degrees of freedom Relativistic ideal gas 9. The Macrocanonical Ensemble Fluctuations in the macrocanonical ensemble III Quantum Statistics 10. Density Operators Fundamentals Pure and mixed states Properties of the density matrix The density operators of quantum statistics 11. The Symmetry Character of Many-Particle Wavefunctions 12. Grand Canonical Description of Ideal Quantum Systems 13. The Ideal Bose Gas Ultrarelativistic Bose gas 14. Ideal Fermi Gas The degenerate Fermi gas Supplement: Natural units 15. Applications of Relativistic Bose and Fermi Gases Quark-gluon plasma in the Big Bang and in heavy-ion collisions IV Real Gases and Phase Transitions 16. Real Gases For absorption: Mayer's cluster expansion Virial expansion 17. Classification of Phase Transitions Theorem of corresponding states Critical indices Examples for phase transitions 18. The Models of Ising and Helsenberg Index