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Explore advanced concepts in statistical mechanics through this lecture examining large deviations theory applied to non-equilibrium diffusive systems, delivered by Bernard Derrida at the Galileo Galilei Institute. Delve into the mathematical framework governing rare fluctuations in systems far from thermal equilibrium, focusing on diffusive processes that exhibit non-trivial statistical behavior. Learn how large deviation principles provide powerful tools for understanding the probability of atypical events in driven systems, boundary-driven processes, and other non-equilibrium scenarios. Examine specific examples of diffusive systems including exclusion processes, reaction-diffusion models, and systems with particle currents, while discovering how macroscopic fluctuation theory connects microscopic dynamics to large-scale statistical properties. Gain insights into the mathematical techniques used to calculate rate functions, understand the role of additivity principle in non-equilibrium systems, and explore connections between large deviations and thermodynamic formalism in the context of driven diffusive systems.
