Lectures 1. (4 h) Stochastic processes, Markov chains and Langevin equation. 2. (4 h) Entropy vs. information. Probability distribution of maximal entropy. 3. (4 h) Description of statistical systems. Evolution and equilibrium states. Liouville equation. Thermodynamic formalisms. 4. (4 h) Thermodynamics of gas systems: a) perfect gas b) nonideal gases (virial expansion, mean field theory) 5. (4 h) Thermodynamics of magnetic systems: a) paramagnetics and Curie law b) Ising model of nearest neighbours interaction c) phase transition in a Curie-Weis-Kac model 6. (2 h) Grand canonical ensemble and theory of phase transitions 7. (2 h) Quantum Statistical systems: a) formalism of statistical quantum mechanics, b) open systems and semigroup dynamics b) multilevel system: Bose-Einstein and Fermi-Dirac statistics 8. (6 h) Thermodynamics of quantum gases a) electron gas in metal, Fermi energy b) relativistic electron gas, stability of white dwarfs c) Bose-Einstein condensation, nonlinear Gross-Pitayevski equation d) photonic gas and thermal radiation e) phonons and crystals Exercises: 1. (2 h) Random variables and their properties. 2. (2 h) Stochastic matrices and Markov evolution. 3. (2 h) Combinatorics of quantum statistics. 4. (2 h) Evolution of a system of N harmonic oscillators. 5. (2 h) Gibbs distribution. Velocity distribution. Doppler broadening of line shapes. 6. (2 h) Virial expansions for thermodynamic parameters. 7. (2 h) Joule-Thompson process 8. (2 h) Correlation function in Ising model. 9. (2 h) Classical and quantum entropy and their properties. Klein inequality. 10. (4 h) Entanglement and quantum correlations. 11. (4 h) Thermal radiation. Planck distribution. Wien law. Stefan-Boltzmann law.
