  This note presents Godunov variables and 4-potentials for the relativistic
Euler equations of barotropic fluids. The associated additional conservation/
production law has different interpretations for different fluids. In
particular it refers to ENTROPY in the case of thermobarotropic fluids, and to
MATTER in the case of isentropic fluids. The paper also presents an explicit
formula for the generating function of the Euler equations in the case of ideal
gases. It pursues ideas on symmetric hyperbolicity going back to Godunov (cf.
also Lax and Friedrichs as well as Boillat) that were elaborated as Ruggeri and
Strumia's theory of convex covariant density systems.
