Uniqueness of Landau-Lifshitz Energy Frame in Relativistic Dissipative Hydrodynamics

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.