Uniqueness of Landau-Lifshitz Energy Frame in Relativistic Dissipative Hydrodynamics

TL;DR

This paper demonstrates that the relativistic dissipative hydrodynamic equations derived from the Boltzmann equation are uniquely consistent with the Landau-Lifshitz energy frame, emphasizing the importance of the macroscopic-frame vector's independence from particle momenta.

Contribution

It proves the uniqueness of the Landau-Lifshitz energy frame in relativistic hydrodynamics derived from kinetic theory under specific conditions.

Findings

Relativistic hydrodynamics equations are uniquely consistent with the Landau-Lifshitz energy frame.

The macroscopic-frame vector must be independent of particle momenta for consistency.

The energy frame is necessary for hydrodynamics to align with the underlying kinetic theory.

Abstract

We show that the relativistic dissipative hydrodynamic equation derived from the relativistic Boltzmann equation by the renormalization-group method uniquely leads to the one in the energy frame proposed by Landau and Lifshitz, provided that the macroscopic-frame vector, which defines the local rest frame of the fluid velocity, is independent of the momenta of constituent particles, as it should. We argue that the relativistic hydrodynamic equations for viscous fluids must be defined on the energy frame if it is consistent with the underlying relativistic kinetic equation.