A numerical and analytical study of the fluctuations of injected power, internal energy/heat currents and other transport observables in realistic and simplified models of fluidized granular matter is proposed. Fluidized granular matter is the class of sys tems made of many grains (from sand to seeds and pills) under a continuous external driving, such as violent shaking of the container. At high fluidization the behavior of such a vibrated granular system resembles that of a gas with inelastic collisions. A granulas system becomes, therefore, the perfect istance of non-equilibrium statistically statitionary system, where the stationarity results from the balance of injected energy and heat dissipated in collisions. Recent experiments have suggested that in a a granular gas a relation similar to the Gallavotti-Cohen Fluctuation Theorem is valid. Some more recent work has shown that false verification of the Fluctuation Theorem are extreme likely to appear in experiments and in numerical simulations, because of the limited range available in the statistics of measured observables. This project aims to study in detail the statistical properties of injected power and internal energy/heat currents and at the same time find a definition of entropy production which c an be suitable for experimentable situations. This ambition is relevant for the whole theory of non-equilibrium statistiscal mechanics.
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