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

TL;DR

This paper reviews the stability issues in relativistic thermodynamics and introduces a unified effective field theory approach, UEIT, which ensures the stability of various thermodynamic models by construction based on the second law.

Contribution

It proposes the Unified Extended Irreversible Thermodynamics (UEIT), a formalism that unifies and stabilizes different relativistic thermodynamic theories through an effective field theory framework.

Findings

Identifies the mathematical origin of instability in relativistic thermodynamics.

Shows that stability of models like Israel-Stewart is guaranteed by the second law.

Provides a unified formalism encompassing multiple thermodynamic theories.

Abstract

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. In particular, the theory aims at modelling 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. Although in Newtonian physics this task can be achieved with a first-order approach to dissipation (i.e. 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. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. We call this approach Unified Extended Irreversible Thermodynamics (UEIT), because it contains, as particular cases, EIT itself, in particular the Israel-Stewart theory and the divergence-type theories, plus Carter's approach and most branches of non-equilibrium thermodynamics, such as relativistic chemistry and radiation hydrodynamics. We use this formalism to explain why all these theories are stable by construction (provided that the microscopic input is correct), showing that their (Lyapunov) stability is a direct consequence of the second law of thermodynamics.