Stationary state of a heated granular gas: fate of the usual   H-functional
  We consider the characterization of the nonequilibrium stationary state of a randomly-driven granular gas in terms of an entropy-production based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the non-equilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed. 
Ioana Bena, Francois Coppex, Michel Droz, Paolo Visco, Emmanuel   Trizac, Frederic van Wijland