  The authors present a study of the non equilibrium statistical properties of
a one dimensional hard-rod fluid dissipating energy via inelastic collisions
and subject to the action of a Gaussian heat bath, simulating an external
driving mechanism. They show that the description of the fluid based on the
one-particle phase-space reduced distribution function, in principle necessary
because of the presence of velocity dependent collisional dissipation, can be
contracted to a simpler description in configurational space. Indeed, by means
of a multiple-time scale method the authors derive a self-consistent governing
equation for the particle density distribution function. This equation is
similar to the dynamic density functional equation employed in the study of
colloids, but contains additional terms taking into account the inelastic
nature of the fluid. Such terms cannot be derived from a Liapunov generating
functional and contribute not only to the relaxational properties, but also to
the non equilibrium steady state properties. A validation of the theory against
molecular dynamics simulations is presented in a series of cases, and good
agreement is found.
