The idea of introducing a compressibility for vibrated granular fluid was already used in ref. [22] in the context of hydrodynamical stability analysis. In a molecular system at equilibrium, the isothermal compressibility is related with the volume fluctuations by where k$_{B}$ is the Boltzmann constant. In non-equilibrium states, there is no reason to expect the above relationship to hold, but it is tempting to employ it to define an effective temper- ature parameter of the system, T$_{eff}$ , expecting it to have some intrinsic physical meaning. Therefore, taking into account that the volume fluctuations in the case being considered are associated to fluctuations of the position Z of the movable piston, we define T$_{eff}$ through The Boltzmann constant has been set equal to unity as it is usually done when defining the granular temperature from the average kinetic energy of the grains. From Eq. (12) it follows that T$_{eff}$ relates the volume response to a pressure perturbations with the steady volume fluctuations of the system. Of course, Eq. (12) by itself is just a mathematical definition and does not add anything to the physical understanding of the system. On the other hand, the definition would become relevant if this effective temperature were related to other temperature-like parameters of the system. Two main candidates clearly stand out: the granular temperature of the gas in the vicinity of the piston, T$_{L}$ , and the temperature parameter of the piston, T$_{P}$ , defined through T$_{P}$ = M < V 2 z > [19]. Both parameters, T$_{L}$ and T$_{P}$ , are not at all the same, as it should be the case if the system under consideration were at equilibrium and energy equipartition would apply. Violation of equipartition is a general feature of granular systems known since long ago [23] and that has attracted a lot of attention in the last years. A more detailed discussion of this issue for the set up being considered here is given in [14]. In Fig. 5, event driven simulation results for the ratio T$_{P}$/T$_{L}$ are plotted as a function of M/m . Several values of the coefficient of normal restitution of the gas in the interval 0 . 85 ≤ α ≤ 0 . 98 have been considered, while again α$_{P}$ = 0 . 99 for all the data shown. It is observed that the behavior of this temperature ratio is quite intricate. 13 σ 2 Z = $_{−}$T$_{eff}$ g 0 ( ∂L ∂M )$_{v}$$_{W}$ . (12) σ 2 V ≡ < ( V − < V > ) 2 > = k$_{B}$T < V > k$_{T}$, (11) k$_{T}$ = − 1 < V > ( ∂ < V > ∂p )$_{T}$ (10)