Volume fluctuations and compressibility of a vibrated granular gas J. Javier Brey and M.J. Ruiz-Montero F´ısica Te´ orica, Universidad de Sevilla, Apartado de Correos 1065, E-41080, Sevilla, Spain (Dated: October 29, 2018) The volume fluctuations in the steady state reached by a vibrated granular gas of hard particles confined by a movable piston on the top are investigated by means of event driven simulations. Also, a compressibility factor, measuring the response in volume of the system to a change in the mass of the piston, is introduced and measured. From the second moment of the volume fluctuations and the compressibility factor, an effective temperature is defined, by using the same relation as obeyed by equilibrium molecular systems. The interpretation of this effective temperature and its relationship with the granular temperature of the gas, and also with the velocity fluctuations of the movable piston, is discussed. It is found that the ratio of the temperature based on the volume fluctuations to the temperature based on the piston kinetic energy, obeys simple dependencies on the inelasticity and on the piston-particle mass ratio. PACS numbers: 45.70.-n,47.70.Nd,51.10.+y arXiv:1002.0542v1 [cond-mat.stat-mech] 2 Feb 2010 Abstract 1