Stability analysis for a thermodynamically consistent model of relativistic fluid dynamics

TL;DR

This paper performs a linear stability analysis of a relativistic fluid dynamics model based on the GENERIC framework, demonstrating that thermodynamic admissibility ensures stability across all relevant parameters.

Contribution

It introduces a stability analysis for a relativistic fluid model grounded in the GENERIC framework, linking thermodynamic admissibility to stability.

Findings

Full thermodynamic admissibility guarantees stability in the model.

Stability holds across the entire range of physically meaningful parameters.

The analysis highlights fundamental differences between liquids and gases in relativistic contexts.

Abstract

The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In relativistic fluid mechanics, positive entropy production is known to be insufficient for guaranteeing stability. Much more restrictive criteria for thermodynamic admissibility have become available in nonequilibrium thermodynamics. We here perform a linear stability analysis for a model of relativistic hydrodynamics that is based on the GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) framework of nonequilibrium thermodynamics. Assuming a simple form of the entropy function, we find stability for the entire range of physically meaningful model parameters. For relativistic fluid dynamics, full thermodynamic admissibility indeed leads to stability.