Classical irreversible thermodynamics versus extended irreversible thermodynamics. The role of the continuity equation

This brief note focuses on a simple fluid, i.e., a homogeneous, chemically inert, and electrically neutral fluid, for which, in the linear non-equilibrium regime, the thermodynamic state is expressed by a relation between pressure, temperature, and density. The approach based on the elementary scales is used to check the validity range of both the classical irreversible thermodynamics and the extended irreversible thermodynamics. The achieved result reveals that the classical irreversible thermodynamics fails in providing arm adequate response when the mechanical solicitations exceed limit values.