Statistical mechanics of a gas-fluidized particle

Characterization of the microscopic fluctuations in systems that are far from equilibrium is crucial for understanding the macroscopic response. One approach is to use an 'effective temperature'--such a quantity has been invoked for chaotic fluids, spin glasses, glasses and colloids, as well as non-thermal systems such as flowing granular materials and foams. We therefore ask to what extent the concept of effective temperature is valid. Here we investigate this question experimentally in a simple system consisting of a sphere placed on a fine screen in an upward flow of gas; the sphere rolls because of the turbulence it generates in the gas stream. In contrast to many-particle systems, in which it is difficult to measure and predict fluctuations, our system has no particle-particle interactions and its dynamics can be captured fully by video imaging. Surprisingly, we find that the sphere behaves exactly like a harmonically bound brownian particle. The random driving force and frequency-dependent drag satisfy the fluctuation-dissipation relation, a cornerstone of statistical mechanics. The statistical mechanics of near-equilibrium systems is therefore unexpectedly useful for studying at least some classes of systems that are driven far from equilibrium.