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The authors present a study of the non equilibrium statistical properties ofa one dimensional hard-rod fluid dissipating energy via inelastic collisionsand subject to the action of a Gaussian heat bath, simulating an externaldriving mechanism. They show that the description of the fluid based on theone-particle phase-space reduced distribution function, in principle necessarybecause of the presence of velocity dependent collisional dissipation, can becontracted to a simpler description in configurational space. Indeed, by meansof a multiple-time scale method the authors derive a self-consistent governingequation for the particle density distribution function. This equation issimilar to the dynamic density functional equation employed in the study ofcolloids, but contains additional terms taking into account the inelasticnature of the fluid. Such terms cannot be derived from a Liapunov generatingfunctional and contribute not only to the relaxational properties, but also tothe non equilibrium steady state properties. A validation of the theory againstmolecular dynamics simulations is presented in a series of cases, and goodagreement is found.

Theory of thermostatted inhomogeneous granular fluids: a self-consistent density functional description