Unified Extended Irreversible Thermodynamics and the Stability of Relativistic Theories for Dissipation

In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize principles non-equilibrium thermodynamics domain fluid dynamics. particular, theory aims at modelling any diffusion-type process (like heat as diffusion energy, viscosity momentum, charge-conductivity particles) directly from thermodynamic laws. Although in Newtonian physics this task can be achieved with first-order approach dissipation (i.e. Navier-Stokes-Fourier like equations), framework relativity simultaneity poses serious challenges methodology, originating instabilities which are, instead, naturally eliminated within EIT. The first part work dedicated reviewing most recent progress made understanding mathematical origin instability problem. second part, we present formalism that arises by promoting classical effective field theory. We call Unified (UEIT), because it contains, particular cases, EIT itself, Israel-Stewart and divergence-type theories, plus Carter's branches thermodynamics, such chemistry radiation hydrodynamics. use explain why all these theories are stable construction (provided microscopic input correct), showing their (Lyapunov) stability direct consequence law thermodynamics.