a consequence, the transverse gluon and (anti)quark entropy density contributions have to increase in comparison to the eQP in order for the sum of the partial entropy densities to describe the same lattice data as the eQP (see Figure \[fig:sHTL contributions\], right). This not only allows for a pure quasiparticle entropy contribution much closer to the Stefan-Boltzmann limit than in the eQP but also proves to have a positive impact on the extension to nonzero chemical potential.

Solution of the flow equation
-----------------------------

Solving the flow equation (\[eq:floweq\]) with coefficients listed in Appendix \[app:flow eq coeff\] the characteristics are found to be well-behaving, as can be seen in Figure \[fig:HTL characteristics\]. Also a stronger curvature of the full HTL characteristics compared to the eQP characteristics (shown as dashed lines in the right panel) is observable.

To explain the disappearance of the ambiguities caused by crossing characteristics in the eQP we mention that the crossings appear due to the effective coupling $G^{2}$ being too large near the pseudocritical temperature [@Blu04]. Since the entropy density increases with decreasing mass parameters $m_{D}^{2}$ and $\hat{M}^{2}$ (which are proportional to $G^{2}T^{2}$ at $\mu=0$) the crossings would therefore disappear for a larger eQP entropy density. One 