Applying the Gibbs stability criterion to relativistic hydrodynamics

TL;DR

This paper introduces a systematic method based on the maximum entropy principle to construct Lyapunov functionals for assessing the stability of equilibrium states in relativistic hydrodynamics, addressing a longstanding challenge.

Contribution

The authors develop a rigorous, systematic technique for deriving stability functionals in relativistic fluids, improving upon previous guesswork-based methods and clarifying physical interpretations.

Findings

Method successfully reproduces known functionals

Applicable when an entropy current with non-negative divergence exists

Advances understanding of relativistic dissipation stability

Abstract

The stability of the equilibrium state is one of the crucial tests a hydrodynamic theory needs to pass. A widespread technique to study this property consists of searching for a Lyapunov function of the linearised theory, in the form of a quadratic energy-like functional. For relativistic fluids, the explicit expression of such a functional is often found by guessing and lacks a clear physical interpretation. We present a quick, rigorous and systematic technique for constructing the functional of a generic relativistic fluid theory, based on the maximum entropy principle. The method gives the expected result in those cases in which the functional was already known. For the method to be applicable, there must be an entropy current with non-negative four-divergence. This result is an important step towards a definitive resolution of the major open problems connected with relativistic dissipation.