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

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.

30 pages, 3 figures. This review article is part of the special issue "Neutron Star Physics in the Multi-Messenger Discourse" for Frontiers Astronomy and Space Science, see https://www.frontiersin.org/articles/10.3389/fspas.2021.686344/abstract

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• Symmetric-hyperbolic quasi-hydrodynamics
• Stability and causality of Carter's multifluid theory
• Relativistic Liquids: GENERIC or EIT?
• Relativistic Bulk Rheology: From Neutron Star Mergers to Viscous Cosmology
• Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?
• The regime of applicability of Israel-Stewart hydrodynamics
• A covariant approach to relativistic large-eddy simulations: The fibration picture
• Universality Classes of Relativistic Fluid Dynamics: Foundations
• Relativistic bulk viscous fluids of Burgers type and their presence in neutron stars
• Gapless non-hydrodynamic modes in relativistic kinetic theory
• Transport coefficients of magnetized neutron star cores
• Universality Classes of Relativistic Fluid Dynamics: Applications
• First-order relativistic hydrodynamics with an information current
• Higher-level large-eddy filtering strategy for general relativistic fluid simulations
• Dispersion relations of relativistic radiation hydrodynamics
• Noncovariant parabolic theories of relativistic diffusion
• Thermodynamic stability implies causality
• Boosting unstable particles
• Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality
• Lorentz-boosted diffusion: initial value formulation and exact solutions
• Extending Israel and Stewart hydrodynamics to relativistic superfluids via Carter's multifluid approach
• The diffusion equation is compatible with special relativity