  Non-equilibrium fluid dynamics derived from the extended irreversible
thermodynamics of the causal M\"uller--Israel--Stewart theory of dissipative
processes in relativistic fluids based on Grad's moment method is applied to
the study of the dynamics of hot matter produced in ultra--relativistic heavy
ion collisions. The temperature, energy density and entropy evolution are
investigated in the framework of the Bjorken boost--invariant scaling limit.
The results of these second order theories are compared to those of first order
theories due to Eckart and to Landau and Lifshitz and those of zeroth order
(perfect fluid) due to Euler. In the presence of dissipation perfect fluid
dynamics is no longer valid in describing the evolution of the matter. First
order theories fail in the early stages of evolution. Second order theories
give a better description in good agreement with transport models. It is shown
in which region the Navier--Stokes--Fourier laws (first order theories) are a
reasonable limiting case of the more general extended thermodynamics (second
order theories).
