Origin of the anomalous heat current in collisional granular fluids
  We present a heuristic explanation for the anomalous (density-gradient-dependent) heat current in collisional granular fluids. Inelastic grain collisions lead to highly non-equilibrium states which are characterized by large spatial gradients and/or temporal variations in the granular temperature. It is argued that the heat current in such non-equilibrium states is driven by the temperature gradient averaged over the typical collision time and/or mean free path. Due to the density dependence of the inelastic energy loss, the nonlocal averaging of the temperature gradient leads to an effective dependence of the heat current upon the density gradient. 
D. Candela and R. L. Walsworth