The balance laws of Rational Extended Thermodynamics describe well the evolution of rarefied gases in non-equilibrium. Usually, it is necessary to approximate the theory in a neighborhood of an equilibrium state and consequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of the field variables, called hyperbolicity region. The goal of this paper is first to determine the differential system with 14 fields for a rarefied polyatomic polytropic gas, approximated at the second-order in the non-equilibrium variables. Then, we investigate and compare the hyperbolicity property of the first-order and second-order systems. In particular, we analyze the role played by the dynamic pressure and the molecular degrees of freedom. Finally, we also show that in the monatomic singular limit the quadratic theory for a polyatomic gas converges to the corresponding quadratic theory for a monatomic gas.

有理扩展热力学的平衡定律很好地描述了非平衡态稀有气体的演化。通常，有必要在平衡状态附近近似该理论，因此，其双曲性仅在称为双曲区域的场变量平衡状态附近才有效。。本文的目标是首先确定稀有多原子多方气体的14个场的微分系统，该系统在非平衡变量中近似于二阶。然后，我们研究和比较一阶和二阶系统的双曲性质。特别是，我们分析了动压和分子自由度所起的作用。最后，我们还表明，在单原子奇异极限下，多原子气体的二次理论收敛于相应的单原子气体二次理论。