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Explore a comprehensive lecture on large deviations for conservative, stochastic partial differential equations (PDEs) and non-equilibrium systems. Delve into the macroscopic fluctuation theory and its role in far-from-equilibrium thermodynamics, focusing on the fundamental formula for large fluctuations around local equilibria. Examine the connection between far-from-equilibrium behavior and zero-noise large deviations in conservative, stochastic PDEs. Investigate a rigorous justification of this relationship using the zero-range process as a case study. Learn about the Gamma-convergence of rate functions to approximating stochastic PDEs and the well-posedness of the skeleton equation, a degenerate parabolic-hyperbolic PDE with irregular coefficients. Discover how DiPerna-Lions' renormalization techniques are extended to nonlinear PDEs in this context.
