Monatomic limit of relativistic extended thermodynamics of polyatomic gas

In a recent paper Pennisi and Ruggeri (Ann Phys 377:414-445, 2017. 10.1016/j.aop.2016.12.012) proposed a casual hyperbolic model for a dissipative polyatomic relativistic gas. The closure was obtained using the maximum entropy principle for the generalized moments of a distribution function that, as in the classical case, depends on an additional continuous variable representing the energy of the internal modes of a molecule; this permits the theory to take into account the energy exchange between translational modes and internal modes of a molecule. The closure depends on a parameter a>-1 that is related to the degrees of freedom of gas. In this paper it is proven that in the singular limit for a-1 the field equations converge to the system obtained by relativistic extended thermodynamics theory of monatomic gas by Liu et al. (Ann Phys 169:191, 1986).