Dissipative hydrodynamics for relativistic multi-component systems

TL;DR

This paper derives second-order dissipative hydrodynamic equations for multi-component systems, emphasizing the importance of treating each component separately to accurately determine the system's shear viscosity, impacting quark-gluon plasma analyses.

Contribution

It introduces a framework for deriving hydrodynamic equations for each component in a multi-component system, highlighting the non-trivial relation of shear viscosity to partial pressures.

Findings

Hydrodynamic equations for each component are essential.

Shear viscosity relates to partial pressures, not an external parameter.

Reevaluation needed for QGP viscosity measurements.

Abstract

Second-order dissipative hydrodynamic equations for each component of a multi-component system are derived using the entropy principle. The shear viscosity of the whole system, appearing in the equation summed-up over all components, is related to the partial shear pressures and cannot be considered as an external parameter. We demonstrate that it is essential to solve hydrodynamic equations for each component, instead of treating a mixture as an effective one-component system with a free parameter $\eta/s$. Thus, extractions of the $\eta/s$ value of the QGP at RHIC and LHC have to be reexamined.