Relativistic Extended Thermodynamics of Polyatomic Gases with Rotational and Vibrational Modes

In a recent article, an infinite set of balance equations has been proposed to modelize polyatomic gases with rotational and vibrational modes in a non-relativistic context. To obtain particular cases, it has been truncated to obtain a model with 7 or 15 moments. Here the following objectives are pursued: 1) to obtain the relativistic counterpart of this model, which, at the non-relativistic limit, gives the same balance equations as in the known classical case; 2) to obtain the previous result for the model with an arbitrary but fixed number of moments; and 3) to obtain the closure of the resulting relativistic model so that all the functions appearing in the balance equations are expressed in terms of the independent variables. To achieve these goals, the following methods are used: 1) the principle of entropy is imposed. As a result, it is obtained that the closure is determined up to a single 4-vectorial function, usually called a 4-potential. 2) To determine this last function, a more restrictive principle is imposed, namely the Maximum Entropy Principle (MEP). 3) Since all the functions involved must be expressed in the covariant form so as not to depend on the observer, the Representation Theorems are used. The findings of this article exactly match the goals outlined earlier. They are clearly novel because they have never been achieved before. They can also be considered improvements because, if the aforementioned arbitrary number of moments is restricted to 16, the present work coincides with that already known in literature.