Stationary state volume fluctuations in a granular medium

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions ϕ of postfluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of ϕ exhibits, as a function of ϕ , a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X , a temperaturelike state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A 157, 1080 (1989)].