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Explore fundamental concepts of Statistical Mechanics in this graduate-level lecture from IMPA's 2025 Summer School, delivered in Portuguese by Professor Hubert Lacoin. Delve into Hamiltonian systems, Liouville's theorem, Poincaré recurrence theorem, Birkhoff's theorem, Boltzmann hypothesis, statistical ensembles, Gibbs measure, Ising model, thermodynamic limit, FKG inequality, phase transitions, phase diagrams, FK models, and Pirogov-Sinai theory. Drawing from key references including Feynman's Statistical Mechanics lectures, Presutti's work on scaling limits, and specialized texts by Friedli and Velenik, master advanced mathematical concepts essential for understanding statistical mechanical systems. Part of a comprehensive master's program series, this lecture offers rigorous mathematical foundations while maintaining accessibility for graduate-level study.
