Relativistic Entropy Inequality

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second order equations which have been introduced in [3]. Since the principle also says that the entropy equation is a scalar equation, this implies, as we show, that one has to take a trace in the energy part of the system. Thus one arrives at the relativistic mass-momentum-energy system for the fluid. In the procedure we use the well-known Liu-M\"uller sum [10] in order to deduce the Gibbs relation and the residual entropy inequality.