Linking the hydrodynamic and kinetic description of a dissipative relativistic conformal theory

We use the entropy production variational method to associate a one-particle distribution function to the assumed known energy-momentum and entropy currents describing a relativistic conformal fluid. Assuming a simple form for the collision operator we find this one-particle distribution function explicitly, and show that this method of linking the hydro and kinetic descriptions is a nontrivial generalization of Grad's ansatz. The resulting constitutive relations are the same as in the conformal dissipative type theories discussed by J. Peralta-Ramos and E. Calzetta [Phys. Rev. D 80, 126002 (2009)]. Our results may prove useful in the description of freeze-out in ultrarelativistic heavy-ion collisions.