Statistical Physics

1. Introductory remarks

2. Brief reminder to thermodynamics
2.1 Laws of thermodynamics
2.2 Consequences from the existence of entropy
2.3 Thermodynamic potentials
2.4 Thermodynamics in static electric and magnetic fields

3. Kinetic Theory
3.1 The classical limit and ideal gas equation of state
3.2 Boltzmann transport equation and H-theorem

4. Statistical mechanics
4.1 Concept of the Gibbsian ensemble
4.2 Microcanonical ensemble
4.2.1 Information entropy
4.2.2 Thermodynamics in the microcanonical ensemble
4.3 Canonical ensemble
4.3.1 Partition function and Helmholtz free energy
4.3.2 Thermodynamics of interaction free systems
4.4 Grandcanonical ensemble
4.4.1 Partition function and grandcanonical potential
4.4.2 Quantum statistics of free particles
4.4.3 Bose-Einstein distribution function
4.4.4 Fermi-Dirac distribution function
4.4.5 Ensemble equivalence in the thermodynamic limit

5. Selected topics and applications of the formalism
5.1 photons, phonons & magnons
5.1.1 Photons and Planck’s black body radiation law
5.1.2 Atomic Vibrations in Solids: phonons
5.1.3 Equipartition theorem
5.1.4 Spin waves and magnons
5.2 Electrons in metals
5.3 Magnetic model systems
5.3.1 Paramagnetism
5.3.2 Ising chain, spin-spin correlation and correlation length
5.3.3 Mean-field theory
5.3.4 Low and high-temperature expansions
5.4 Phase transitions
5.4.1 Phase diagrams
5.4.2 Landau theory 
5.4.3 Critical phenomena

6. Mathematical appendix
6.1 Thermal averages using the density operator