Giacomo Gradenigo, CNR-ISC Roma # Out-of-equilibrium correlations and entropy production in driven granular fluids: theory, simulations and experiments # In a driven granular fluid energy is continuously gained from a thermal bath and lost through inelastic collisions. The irreversible nature of this dynamics produces some correlations between the hydrodynamics fields, that are absent at equilibrium. In this talk we summarize some results on the spectrum of velocity structure factors in a driven granular fluid. This spectrum can be calculated analytically from a standard fluctuating hydrodynamic theory and theoretical predictions are found in good agreement with the results of both event-driven molecular dynamic simulation and real experiments, realized with a monolayer of inelastic beads fluidized with a vertical shaking. We also derive a coarse-grained entropy production formula for granular fluid models, making explicit the dependence of this observable from the out-of-equilibrium correlations between hydrodynamics fields and showing that entropy production strongly depends on the kind of thermostat coupled to the granular fluid.