Advanced Statistical Physics for Master Module Advanced ...

Advanced Statistical Physics for MasterModule Advanced Theoretical Physics II4+2 Lectures per Week, 9 ECTS CreditsContentI. Thermodynamics1. Basic notions and postulates1.1 Nature of thermodynamics1.2 Observables of thermodynamics- Conserved quantities- Averages of microscopic coordinates- Remaining macroscopic influence1.3 Systems and parameters- Simple model systems, V, N 1 …, N k1.4 Internal energy- Mechanical, electrical, thermal- Equilibrium states- Constraints- Heat- 1st Law for simple systems1.5 Entropy postulate: 2nd Law2. Equilibrium conditions2.1 Conjugate variables2.2 Equations of state: energetic, entropic2.3 Thermal equilibrium2.4 Consequences of the homogeneity3. Microscopic explanation of entropy4. The ideal gas and the Carnot cycle5. Thermodynamic potentials5.1 Legendre transform5.2 The potentials5.3 Extremal principles5.4 Maxwell relations6. Stability conditions6.1 Entropic representation6.2 Energetic representation6.3 Further potentials6.4 The Van der Waals Gas6.5 Phase transition of one-component systems6.6 Clausius-Clapeyron, Gibbs Phase rule

II.Statistical mechanics7. Ensembles7.1 Postulates and statements7.2 Micro and macro conditions7.3 Phase space, Liouville´s theorem7.4 Statistical definition of entropy7.5 The microcanonical ensemble8. The canonical ensemble8.1 The Boltzmann factor8.2 Two level system8.3 Free energy8.4 Factorizable systems, Gibb´s paradox8.5 Partition function and integral8.6 The classical ideal gas8.7 Density of states and Debye modelIII.Quantum Statistics9. Fundamentals9.1 Density operator and entropy9.2 Many particle wavefunctions9.3 Grand canonical ensembles10. Ideal quantum gas10.1 Ideal Bose gas10.2 Ideal Fermi gasIV. Real gases and phase transitions11. Real gases11.1 Virial expansion12. Phase transitions12.1 Classification12.2 Critical indices12.3 Examples13. Ising and Heisenberg models