Granular Thermodynamics

We present experimental evidence for a strong analogy between quasi-2D uniform non-equilibrium steady states (NESS) of excited granular materials and equilibrium thermodynamics. Under isochoric conditions we find that the structure of granular NESS, as measured by the radial distribution function, the bond order parameter, and the distribution of Voronoi cells, is the same as that found in equilibrium simulations of hard disks. Three distinct states are found corresponding to a gas, a dense gas, and a crystal. The dynamics of the dense gas is characterized by sub-diffusive behavior on intermediate time scales (caging). Under isobaric conditions we find a sharp first-order phase transition characterized by a discontinuous change in density and granular temperature as a function of excitation strength. The transition shows rate dependent hysteresis but is completely reversible if the excitation strength changes quasi-statically. All of these behaviors are analogous to equilibrium thermodynamics. The one difference is the velocity distributions, which are well described by P(c) = fMB1 + a2S2{c )], in the range —2 < c < 2, where c = vj \2T, v is one component of the velocity, T is the granular temperature, fmb is a Maxwell-Boltzmann and S2 is a second order Sonine polynomial. The single adjustable parameter, a2, is a function of the filling fraction, but not T. For \c\ > 2, P(c) <x exp(—A x c~<) as observed in many other experiments.