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Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider theclassical limit of the relativistic theory of moments associated with theBoltzmann-Chernikov equation truncated at a tensorial index $N+1$ and theyproved that there exists a unique possible choice of the moments in theclassical case for a given $N$ both for monatomic and polyatomic gases. Inparticular, in polyatomic gases, there exists a new hierarchy of moments thatis more general than the one considered in the recent literature. Asconsequence, when $N=2$, in the classical limit, there is a theory with $15$fields. In this paper, we consider this system of moments, and we close thesystem using the maximum entropy principle. It is shown that the theorycontains as a principal subsystem the previously polyatomic $14$ fields theory,and in the monatomic limit, in which the dynamical pressure vanishes, thedifferential system converges instead to Grad 13-moments system to the 14moments theory proposed by Kremer [Annales de l'I.H.P. Physique th\'eorique,45, 419-440 (1986)].

Molecular Extended Thermodynamics of Rarefied Polyatomic Gases with a new Hierarchy of Moments