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Explore advanced concepts in statistical mechanics through this comprehensive lecture on large deviations of non-equilibrium diffusive systems. Delve into the mathematical framework and theoretical foundations that govern the behavior of particles in non-equilibrium states, examining how systems deviate from typical behavior when driven away from thermal equilibrium. Learn about the application of large deviation theory to understand rare events and fluctuations in diffusive processes, including the derivation of rate functions and the analysis of dynamical phase transitions. Investigate the connections between microscopic dynamics and macroscopic observables, with particular emphasis on current fluctuations and density profiles in driven systems. Master the techniques for calculating large deviation functions and understand their physical interpretation in the context of non-equilibrium statistical mechanics, providing essential tools for analyzing complex many-body systems far from equilibrium.
