Relativistic Dissipative Hydrodynamic Equations at the Second Order for Multi-Component Systems with Multiple Conserved Currents

TL;DR

This paper develops second order relativistic dissipative hydrodynamic equations for multi-component systems with multiple conserved currents, extending Israel-Stewart theory and incorporating new terms like thermal diffusion effects.

Contribution

It introduces additional moment equations for conserved currents and derives constitutive equations with novel terms, advancing the theoretical framework for relativistic hydrodynamics.

Findings

Additional moment equations are necessary for consistency.

New constitutive terms include thermal diffusion effects.

Comparison with existing formalisms shows improved consistency.

Abstract

We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.