On the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics

TL;DR

The paper clarifies that generic instabilities in relativistic hydrodynamics stem from coupling heat with acceleration in Eckart's formalism, which contradicts thermodynamic principles, and can be avoided with a different theoretical approach.

Contribution

It demonstrates that these instabilities are due to Eckart's formalism and proposes a Meixner-like approach to resolve the issue within linear thermodynamics.

Findings

Identifies the origin of instabilities as coupling in Eckart's formalism.

Shows that these are contradictions to thermodynamic postulates.

Suggests a modified approach to avoid such instabilities.

Abstract

It is shown that the so-called generic instabilities that appear in the framework of relativistic linear irreversible thermodynamics, describing the fluctuations of a simple fluid close to equilibrium, arise due to the coupling of heat with hydrodynamic acceleration which appears in Eckart's formalism of relativistic irreversible thermodynamics. Further, we emphasize that such behavior should be interpreted as a contradiction to the postulates of linear irreversible thermodynamics (LIT), namely a violation of Onsager's hypothesis on the regression of fluctuations, and not as fluid instabilities. Such contradictions can be avoided within a relativistic linear framework if a Meixner-like approach to the phenomenological equations is employed.