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Statistical mechanics starts as a theory of fluctuations. Its foundations are found in the theory of large deviations. Its development for non-equilibrium purposes requires a fine combination of probabilistic and analytical methods. Moreover mathematical precision is extremely helpful for understanding some subtle conceptual points related to the origin of irreversibility and to the precise properties of entropy (production) functionals. For genuine non-equilibrium situations, the workshop will clarify the mathematical properties of a linear response theory and of the canonical structure of static and dynamical fluctuations. Applications are found in the theory of complex systems, where the mathematical structure of a diversity of problems can be related to the structure of fluctuations and the response. Specific topics include:

-discussions on a rigorous fluctuation theory in perturbative order around non-equilibrium and its relationship to the response of the system;
-systematic mathematical corrections to local equilibrium in the derivation of hydrodynamic and kinetic equations.