Extensivity of Irreversible Current and Stability in Causal Dissipative Hydrodynamics

TL;DR

This paper extends causal dissipative hydrodynamics to ultra-relativistic regimes by incorporating extensiveness of irreversible currents, introducing a non-linear viscosity suppression term that enhances stability and aligns fluid behavior closer to ideal fluids.

Contribution

The authors develop a new formulation of causal dissipative hydrodynamics applicable to ultra-relativistic conditions, including a non-linear term for viscosity suppression, differing from the Israel-Stewart theory.

Findings

The new equation stabilizes numerical calculations in ultra-relativistic conditions.

Viscosity effects are suppressed, making the fluid behave more like an ideal fluid.

The formulation aligns with extended irreversible thermodynamics but differs from Israel-Stewart theory.

Abstract

We extended our formulation of causal dissipative hydrodynamics [T. Koide \textit{et al.}, Phys. Rev. \textbf{C75}, 034909 (2007)] to be applicable to the ultra-relativistic regime by considering the extensiveness of irreversible currents. The new equation has a non-linear term which suppresses the effect of viscosity. We found that such a term is necessary to guarantee the positive definiteness of the inertia term and stabilize numerical calculations in ultra-relativistic initial conditions. Because of the suppression of the viscosity, the behavior of the fluid is more close to that of the ideal fluid. Our result is essentially same as that from the extended irreversible thermodynamics, but is different from the Israel-Stewart theory. A possible origin of the difference is discussed.