Classical Limit of Relativistic Moments Associated with Boltzmann–Chernikov Equation: Optimal Choice of Moments in Classical Theory

The moment system associated with the Boltzmann equation is largely used in many applications and is the main ingredient of Rational Extended Thermodynamics (RET). The choice of truncation of moments is arbitrary and many possibilities are present in the literature depending in particular on many contracted indexes in each moment tensor considered. Moreover, in a polyatomic gas, we have two hierarchies of moments with different indexes of truncation. As any classical theory can be considered as a limiting case of a relativistic one, we study in this paper the moments associated with the relativistic Boltzmann–Chernikov equation until the index of truncation N. We take the classical limit for both polyatomic and monatomic rarefied gases and prove that there exists only unique possible choice of the moments in the classical case for a given N.