  We consider the complete Euler system describing the time evolution of a
general inviscid compressible fluid. We introduce a new concept of
measure-valued solution based on the total energy balance and entropy
inequality for the physical entropy without any renormalization. This class of
so-called dissipative measure-valued solutions is large enough to include the
vanishing dissipation limits of the Navier-Stokes-Fourier system. Our main
result states that any sequence of weak solutions to the Navier-Stokes-Fourier
system with vanishing viscosity and heat conductivity coefficients generates a
dissipative measure-valued solution of the Euler system under some physically
grounded constitutive relations. Finally, we discuss the same asymptotic limit
for the bi-velocity fluid model introduced by H.Brenner.
