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In a relativistic context, the main purpose of Extended IrreversibleThermodynamics (EIT) is to generalize the principles of non-equilibriumthermodynamics to the domain of fluid dynamics. In particular, the theory aimsat modelling any diffusion-type process (like heat as diffusion of energy,viscosity as diffusion of momentum, charge-conductivity as diffusion ofparticles) directly from thermodynamic laws. Although in Newtonian physics thistask can be achieved with a first-order approach to dissipation (i.e.Navier-Stokes-Fourier like equations), in a relativistic framework therelativity of simultaneity poses serious challenges to the first-ordermethodology, originating instabilities which are, instead, naturally eliminatedwithin EIT. The first part of this work is dedicated to reviewing the mostrecent progress made in understanding the mathematical origin of thisinstability problem. In the second part, we present the formalism that arisesby promoting non-equilibrium thermodynamics to a classical effective fieldtheory. We call this approach Unified Extended Irreversible Thermodynamics(UEIT), because it contains, as particular cases, EIT itself, in particular theIsrael-Stewart theory and the divergence-type theories, plus Carter's approachand most branches of non-equilibrium thermodynamics, such as relativisticchemistry and radiation hydrodynamics. We use this formalism to explain why allthese theories are stable by construction (provided that the microscopic inputis correct), showing that their (Lyapunov) stability is a direct consequence ofthe second law of thermodynamics.

Unified Extended Irreversible Thermodynamics and the stability of relativistic theories for dissipation