Thermodynamic coefficients in third-order relativistic fluid dynamics
We developed the third-order hydrodynamic equations using relativistic extended thermodynamics of gases with 14 independent fields. The resulting fluid equations are based on the relativity principle, the entropy principle, and the requirement of hyperbolic, and hence finite, propagation of disturbances, which is automatically incorporated. The expressions of entropy, four-current, shear-stress tensor, dynamic pressure, and heat flux are expanded up to third order (cubic). We explicitly present the newly calculated coefficients in the equilibrium properties of an ultra-relativistic gas regime and the non-degenerate relativistic gas. Contrary to the general cases, the non-degenerate regime eliminates fugacity from the coefficients, allowing for the easy normalization of these coefficients, and the ultra-relativistic regime provides us with the upper bounds of these coefficients. We found good agreement on some of the coefficients as compared to calculations from earlier models, specifically in kinetic theory, and other coefficients had slightly different values to those obtained in kinetic theory.