A CAUSAL STATISTICAL FAMILY OF DISSIPATIVE DIVERGENCE-TYPE FLUIDS

We define a particular class of dissipative relativistic fluid theorie s of divergence type with a statistical origin, in the sense that the three tensor fields appearing in the theory can be expressed as the fi rst three moments of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperboli c partial differential equations is very simple and allows one to iden tify a subclass of manifestly causal theories, which are so for all st ates outside equilibrium for which the theory preserves this statistic al interpretation condition. This subclass includes the usual equilibr ium distributions, namely Boltzmann, Bose or Fermi distributions, acco rding to the statistics used, suitably generalized outside equilibrium . Therefore, this gives a simple proof that they are causal in a neigh bourhood of equilibrium Unfortunately, these theories cannot retain th eir statistical character over the whole manifold of non-equilibrium s tates. Indeed, as we shall show, they cannot even be defined in any wh ole neighbourhood containing the equilibrium submanifold. This fact le ads us to speculate that a possible origin of this behaviour is an inc onsistency between the 14-parameter Grad truncation and the requiremen t of the existence of an entropy law. We also define a particular clas s of dissipative divergence-type theories with only a pseudostatistica l origin. Some elements of this class do not have the previous inconsi stency between the 14-parameter Grad truncation and the requirement of the existence of an entropy law. The set of pseudostatistical theorie s also contains a subclass (including the one already mentioned) of ma nifestly causal theories.