the Eckart frame (dotted line).[]{data-label="fig:4"}](dnbdy.pdf "fig:"){width="3.3in"} ![The rapidity distributions of net baryon number (a) without and (b) with $\delta f$ correction at freeze-out for the ideal hydrodynamic system (solid line) compared to those for the systems with baryon diffusion in the Landau frame (dashed line) and with energy dissipation in the Eckart frame (dotted line).[]{data-label="fig:4"}](dnbdy_df.pdf "fig:"){width="3.3in"}

It is worth noting that the effect of the $\delta f$ correction is larger in the Eckart frame for the charged particle distribution while it is larger in the Landau frame for the net baryon distribution (Fig. \[fig:5\]). The results suggest that an adequate treatment of $\delta f$ corrections are important for qualitative understanding of the flow observables.

![The ratios of the rapidity distributions with and without $\delta f$ correction for (a) charged particles and (b) for net baryon number in the Landau frame (dashed line) and in the Eckart frame (dotted line).[]{data-label="fig:5"}](dnchdy_ratio.pdf "fig:"){width="3.2in"} ![The ratios of the rapidity distributions with and without $\delta f$ correction for (a) charged particles and (b) for net baryon number in the Landau frame (dashed line) and in the Eckart frame (dotted line).[]{data-label="fig:5"}](dnbdy_ratio.pdf "fig:"){width="3.2in"}

Discussion and Conclusions {#sec5}
==========================

The baryon diffusive and the energy dissipative hydrodynamics at 