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 fluids1,2, spin glasses3,4, glasses5,6 and colloids7,8, as well as non-thermal systems such as flowing granular materials9,10,11,12,13,14 and foams15. 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.