| Finding out the appropriate set of macroscopic variables that characterizes the equilibrium state of a given system is the first step of any thermodynamic study. What these variables are for a sample of sand in a box is still under discussion. Several studies have suggested that the number of grains, N, and the apparent volume, V, suffice to define equilibrium states in tapped granular samples. Tapping provides the energy necessary to allow the system explore different deposited configurations over which macroscopic observables can be averaged. A large number of taps are necessary to guarantee that the stationary (equilibrium) state is reached. Here, we show that N and V do not determine univocally such equilibrium states, which compels us to invoke other macroscopic variables. Recent theoretical proposals suggest that the force moment tensor, Sigma, must be added to the set (i.e., an NVSigma ensemble). We have found that two equilibrium states obtained with different excitations, even if they have same V and N, may present distinct values of Sigma. This result reveals the incomplete picture we have been based upon for over two decades when looking into the equilibrium properties of static granular matter; and takes us one step closer to complete the definition of the relevant state variables. |
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