Symmetric-hyperbolic quasi-hydrodynamics

TL;DR

This paper develops a systematic, symmetric hyperbolic framework for quasi-hydrodynamics, unifying different theories, analyzing non-hydrodynamic modes, and applying the formalism to plasma models and diffusion.

Contribution

It introduces a general, thermodynamically consistent formalism for quasi-hydrodynamics that includes multiple non-hydrodynamic modes and unifies Israel-Stewart theories in different frames.

Findings

Israel-Stewart theories in Eckart and Landau frames are equivalent in the linear regime.

Non-equilibrium degrees of freedom in strongly coupled plasmas appear in pairs with opposite phase.

Modified Cattaneo's model aligns initial transient with holographic plasma dynamics.

Abstract

We set up a general framework for systematically building and classifying, in the linear regime, causal and stable dissipative hydrodynamic theories that, alongside with the usual hydrodynamic modes, also allow for an arbitrary number of non-hydrodynamic modes with complex dispersion relation (such theories are often referred to as "quasi-hydrodynamic"). To increase the number of non-hydrodynamic modes one needs to add more effective fields to the model. The system of equations governing this class of quasi-hydrodynamic theories is symmetric hyperbolic, thermodynamically consistent (i.e. the entropy is a Lyapunov function) and can be derived from an action principle. As a first application of the formalism, we prove that, in the linear regime, the Israel-Stewart theory in the Eckart frame and the Israel-Stewart theory in the Landau frame are exactly the same theory. In addition, with an Onsager-Casimir analysis, we show that in strongly coupled plasmas the non-equilibrium degrees of freedom typically appear in pairs, whose members acquire opposite phase under time reversal. We use this insight to modify Cattaneo's model for diffusion, in a way to make its initial transient consistent with the transient dynamics of holographic plasmas.