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Explore the mathematical framework of large deviations theory applied to non-equilibrium diffusive systems in this comprehensive lecture delivered at the Galileo Galilei Institute. Delve into the fundamental principles governing how diffusive systems behave when driven away from thermal equilibrium, examining the statistical mechanics of rare events and fluctuations that deviate significantly from typical behavior. Learn about the theoretical foundations that describe how particles diffuse through media under non-equilibrium conditions, including the mathematical tools and techniques used to analyze large deviation functions. Discover the connections between microscopic dynamics and macroscopic observables in systems where detailed balance is broken, and understand how large deviation theory provides insights into the probability of observing atypical configurations or currents. Gain exposure to advanced concepts in statistical physics that bridge equilibrium and non-equilibrium phenomena, with applications to various physical systems including driven lattice gases, exclusion processes, and other interacting particle systems.
