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Explore advanced concepts in statistical mechanics through this comprehensive lecture on large deviations of non-equilibrium diffusive systems, delivered by renowned physicist Bernard Derrida at the Galileo Galilei Institute. Delve into the mathematical framework and theoretical foundations that govern the behavior of diffusive systems operating far from thermal equilibrium, examining how rare fluctuations and atypical trajectories emerge in these complex systems. Learn about the application of large deviation theory to understand the statistical properties of particle currents, density profiles, and other observables in driven diffusive systems. Discover the connections between microscopic dynamics and macroscopic phenomena, including the role of fluctuation theorems and the emergence of non-trivial phase transitions in the space of trajectories. Gain insights into cutting-edge research methods used to analyze systems such as exclusion processes, reaction-diffusion systems, and other paradigmatic models of non-equilibrium statistical mechanics, while understanding how these theoretical tools apply to real-world phenomena in physics, chemistry, and biology.
