Complete relativistic second-order dissipative hydrodynamics from the entropy principle

TL;DR

This paper derives a comprehensive set of relativistic dissipative hydrodynamic equations using the entropy principle, resolving longstanding ambiguities in transport coefficients and improving the modeling of heavy-ion collision dynamics.

Contribution

It provides a complete derivation of second-order relativistic dissipative hydrodynamics with uniquely determined transport coefficients from a unified framework.

Findings

All second-order transport coefficients are uniquely determined.

Eliminates ambiguity in the relaxation time for bulk viscosity.

Prevents cavitation in one-dimensional expansion even with large bulk viscosity.

Abstract

We present a new derivation of relativistic dissipative hydrodynamic equations, which invokes the second law of thermodynamics for the entropy four-current expressed in terms of the single-particle phase-space distribution function obtained from Grad's 14-moment approximation. This derivation is complete in the sense that all the second-order transport coefficients are uniquely determined within a single theoretical framework. In particular, this removes the long-standing ambiguity in the relaxation time for bulk viscosity thereby eliminating one of the uncertainties in the extraction of the shear viscosity to entropy density ratio from confrontation with the anisotropic flow data in relativistic heavy-ion collisions. We find that in the one-dimensional scaling expansion, these transport coefficients prevent the occurrence of cavitation even for rather large values of the bulk viscosity estimated in lattice QCD.