Stability of multicomponent Israel-Stewart-Maxwell theory for charge diffusion

TL;DR

This paper derives stability criteria for multicomponent Israel-Stewart hydrodynamics with electromagnetic fields, ensuring causality and stability across various equilibrium states, including rotating and charged conditions.

Contribution

It provides a comprehensive stability analysis for Israel-Stewart-Maxwell theory, extending stability conditions to magnetohydrodynamics with electromagnetic interactions.

Findings

Electromagnetic part of the information current is stable and causal.

Stability criteria are valid for all thermodynamic equilibria, including rotating and charged states.

Results extend to magnetohydrodynamics formulations.

Abstract

We obtain stability criteria for diffusive inviscid multicomponent Israel-Stewart hydrodynamics with and without background or dynamic electromagnetic fields. Our analysis is grounded on the maximum entropy principle, and it provides stability conditions that are valid around all thermodynamic equilibria, including rotating equilibria, charged equilibria, and equilibria in a background gravitational field. We prove that the electromagnetic part of the information current is stable and causal by construction and, therefore, the stability criteria found for Israel-Stewart theories of hydrodynamics automatically extend to similar formulations of magnetohydrodynamics.