Energy and power fluctuations in vibrated granular gases

Using two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study the fluctuations of its total kinetic energy, of the power injected into the gas by the moving boundary and of the power dissipated by inelastic collisions. We show that an effective number Nf of degrees of freedom that depends on the inelasticity of collisions can be extracted from the probability density function (PDF) of the fluctuations of the total kinetic energy E. $\langle E \rangle /N_f$ is then an intensive variable contrary to the usually defined granular temperature $T_{gr} = \langle E \rangle / N$. We then show that an intensive temperature can also be calculated from the probability of certain large deviations of the injected power. Finally, we show that the fluctuations of injected and dissipated power are related such that their ratio is inversely proportional to the square-root of the ratio of their correlation times. This allows to define a quantity homogenous to a temperature that is intensive and conserved in the process of energy dynamics from its injection by the driving piston to its dissipation by inelastic collisions