Which moments are appropriate to describe gases with internal structure in Rational Extended Thermodynamics?

TL;DR

This paper introduces a new hierarchy of moments for describing classical polyatomic gases in Rational Extended Thermodynamics, emphasizing the total energy including internal modes, and demonstrates the system's convexity and symmetric form.

Contribution

It proposes a natural physical hierarchy of moments for polyatomic gases, extending previous approaches and establishing a convex, symmetric system using the Maximum Entropy Principle.

Findings

The new hierarchy includes total energy with internal modes.

The system is proven to be convex and can be symmetrized.

The approach generalizes previous moment hierarchies.

Abstract

Motivated by a recent paper of Pennisi (2021) in the relativistic framework, we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differential system of the previous approach is proved to be a \emph{principal subsystem} of the present one. The main idea is that at the molecular level, the total energy is the kinetic energy plus the energy of internal mode due to the rotation and vibration, and the increasing moments contain this total energy as power in which the power index increases with the number of tensorial indexes. In particular, we consider the case of $15$ moments, and we close the system using the variational method of the Maximum Entropy Principle. We prove the convexity of entropy and the possibility to put the system in symmetric form. This more rich kinetic framework may be interesting also as possible applications to biomathematics or other fields in which kinetic models were applied recently with success.