The Course aims at introducing the basic concepts of Statistical Mechanics, in order to bridge the micro- and the macroscopic descriptions of the many body systems. Covered topic include:

• Thermodynamics. We revise the basis of the Equilibrium Thermodynamics, and introduce all the macroscopic physical quantities that will be given a statistical interpretation.
• Kinetic theories. Distribution functions and their evolution. Diluted gas, Boltzmann equation. Basic properties of the solutions of the Boltzmann equation. H theorem and irreversibility. Transport coefficients.
• Classical Statistical Mechanics. Hamiltonian formulation of the motion of a classical system. Liouville equation. Ensemble and time averages. Ergodic problem. Statistical ensembles. Microcanonic and canonic ensemble. Application: Ising spins in 1D and 2D. Mean field theory.
• Complex systems with microstructures. Structured minimizers of non-convex functionals. Application: shape memory alloys.

During the course numeric laboratories will be held, aiming at the learning of Monte-Carlo methods for integral calculus, and for the dynamics of complex systems.

Esame orale e prova di laboratorio numerico.