Advanced statistical physics

Course goals

After following the course, you

• can associate microcanonical, canonical and grand canonical partition functions with thermodynamic potentials and derive corresponding thermodynamic identities. Additionally, you can connect these potentials to each other via Legendre transforms.
• can derive and work with the classical and quantum mechanical distributions for ideal gases.
• can compute thermodynamic quantities for classical non-ideal gases.
• can describe phase transitions of classical particles
• can study phase transitions using mean-field theory. You can also identify scalar order parameters and apply these to phase transitions.

Content

This course explores the principles and applications of thermodynamics and statistical physics, emphasizing the description of classical many-body systems and touching upon a few simple quantum gases. We cover the following topics: phase transitions (gas-liquid condensation, magnetic ordering, crystallization, and phase separation), and the structure and thermodynamic properties of non-ideal gases. The theoretical framework comprises mean-field theory, Landau theory for first- and second-order phase transitions, and the virial expansion for non-ideal atomic gases. In addition, the formal relationship of the various thermodynamic potentials (energy, free energy, enthalpy, Gibbs free energy, and grand potential) are related to each other via Legendre transformations; universal thermodynamic identities are also derived.