the second-order in the Landau and the Eckart frames have been discussed. The system is stable at the second order when the relaxation time is semi-positive in the Landau frame and it is larger than the minimum value in the Eckart frame. The mode analyses implies that causality is also satisfied in the long wave length limit. The transport coefficients of the two frames at the linear and the second order are shown to be related. The full second-order terms are found to be necessary for a consistent matching. The results are generic and independent of the individual derivation method of the hydrodynamic equations of motion.

The frame dependence is tested in a numerical hydrodynamic model of relativistic heavy-ion collisions. The net baryon number is chosen as the conserved charge of the system and the space-time evolutions of a QCD medium in the Landau and the Eckart frames are compared to that of the inviscid system. The space-time rapidity distribution of the entropy density is not much affected by the dissipative currents while that of net baryon density is visibly modified. The effects of the baryon diffusion and the energy dissipation is found to be quantitatively similar for those thermodynamic 