In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. Navier–Stokes–Fourier like equations), in a relativistic framework the relativity of simultaneity poses serious challenges to the first-order methodology, originating instabilities which are, instead, naturally eliminated within EIT. Although in Newtonian physics this task can be achieved with a first-order approach to dissipation (i.e. In particular, the theory aims at modeling any diffusion-type process (like heat as diffusion of energy, viscosity as diffusion of momentum, charge-conductivity as diffusion of particles) directly from thermodynamic laws. In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences, Warszawa, Poland.
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