Structure of entropies in dissipative multicomponent fluids

We investigate the structure of mathematical entropies for dissipative multicomponent fluid models derived from the kinetic theory of gases. The corresponding governing equations notably involve nonideal thermochemistry as well as diffusion fluxes driven by chemical potential gradients and temperature gradients. We obtain the general form of mathematical entropies compatible with the hyperbolic structure of the system of partial differential equations assuming a natural nondegeneracy condition. We next establish that entropies compatible with the hyperbolic-parabolic structure are unique up to an affine transform when they are independent on mass and heat diffusion parameters.