We present a thermodynamic theory of weakly excited two-dimensional granular systems from the viewpoint of elementary excitations of spinless Fermions. We introduce a global temperature $T$ that is associated with the acceleration amplitude $\gamma$ in a vibrating bed. We show that the configurational statistics of weakly excited granular materials in a vibrating bed obey the Fermi statistics.

• Received 7 August 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.2764