-KNOWLEDGE AND UNDERSTANDING: provide the student with the conceptual elements that are fundamental for understanding the thermodynamic properties of macroscopic systems , starting from the microscopic Hamiltonian. - ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING: provide the students with the basic tools to compute partition functions and, from these, the thermodynamic properties of many-body systems; in particular for systems of non-interacting particles, both in the classical and quantum regime. - MAKING JUDGMENTS: make the student able to apply learned concepts and tools in a critical way; checking (i) the logical coherence of solutions and derivations, the correctness of (ii) dimensions and (iii) order of magnitude of calculated quantities. - COMMUNICATION SKILLS: make the student able to explain and transmit to others the learned concepts, being able to frame a specific problem in a broader context. - LEARNING SKILLS: make the student capable of critically learning concepts and solution tools, favoring logical reasoning rather than learning by heart.

Good knowledge of mechanics and thermodynamics, phase space. Practical knowledge of multiple integrals and change of variables, integrals containing exponentials and or gaussians combined with powers, Taylor expansion of the simplest functions (trigonometric, exponential, hyperbolic, logarithm.), geometric series, binomial expansion.

Reminders on thermodynamics and probability theory Phase space. Liouville theorem. Ensemble theory: microcanonical, canonical, grandcanonical. Entropy. Partition function, free energy and derivation of thermodynamics. Cluster expansion. Introduction of simple lattice statistical mechanics models. Basic elements of information theory and connection with the concepts of statistical physics. The perfect gas. Equipartition theorem. Gibbs paradox. Energy fluctuations. Quantum statistical mechanics. Fermi-Dirac and Bose-Enstein quantum statistics for ideal gases. Fermi gas: classical limit; degenerate limit and specific heat at low temperatures; non-interacting fermions at T=0. Bose gas: photons; phonons in solids; Bose-Einstein condensation (BEC).

Statistical Mechanics, second edition, Wiley and Sons, New York, 1987. Supplementary material: first two chapters of M. Mezard and A. Montanari: Information, Physics and Computation

Brief survey of thermodynamics and probability theory. Phase space. Gibbs statistical ensemble. Liouville theorem. Microcanonical ensemble. Entropy. Derivation of thermodynamics. Canonical ensemble. Partition function and free energy. Introduction of simple statistical mechanics models on lattice. Connection with the basic elements of information theory and Shannon's theorems. Microcanonical-canonical equivalence. Grandcanonical ensemble. Fluctuations of the number of particles. Canonical-grandcanonical equivalence. The perfect gas. Equipartition theorem. Gibbs paradox and correct Boltzmann counting. Energy fluctuations. Quantum statistical mechanics. Fermi-Dirac and Bose-Enstein quantum statistics for ideal gases. Classical limit of quantum statistics. Fermi gas: classical limit; degenerate limit and specific heat at low temperatures; non-interacting fermions at T=0. Bose gas: photons; phonons in solids and specific heat at low temperatures; Bose-Einstein condensation (BEC) and calculation of the Bose-Einstein critical temperature of the ideal gas.

Lectures, exercises.

Written and oral exam. The written exam is scored using a grade out of 30, expressed as the sum of the scores for the various exercises. The written exam consists of applied exercises, which in turn involve solving problems on the fundamental topics of the course, requiring considerations based on the understanding of key concepts in statistical physics. The oral exam will be scored out of 30 and consists of verification questions, each of which will be assigned a score. The final grade will be determined by averaging the scores for the written and oral exams. The final grade takes into account the ability to correctly solve and clearly discuss the exercises and topics covered.