On a non approximated approach to Extended Thermodynamics for dense gases and macromolecular fluids

TL;DR

This paper presents a unique, exact non-approximated solution to the 14 moments model in Extended Thermodynamics for dense gases and macromolecular fluids, addressing key physical and mathematical conditions.

Contribution

It proves the uniqueness of the exact solution and derives it without relying on expansions around equilibrium, enhancing understanding of the model.

Findings

Proved the uniqueness of the exact solution.

Derived the solution without equilibrium expansions.

Identified new insights beyond approximate solutions.

Abstract

Recently the 14 moments model of Extended Thermodynamics for dense gases and macromolecular fluids has been considered and an exact solution, of the restrictions imposed by the entropy principle and that of Galilean relativity, has been obtained through a non relativistic limit. Here we prove uniqueness of the above solution and exploit other pertinent conditions such us the convexity of the function $h'$ related to the entropy density, the problem of subsystems and the fact that the flux in the conservation law of mass must be the moment of order 1 in the conservation law of momentum. Also the solution of this last condition is here obtained without using expansions around equilibrium. The results present interesting aspects which were not suspected when only approximated solutions of this problem were known.