means to impose the Maxwell relation $\partial s/\partial\mu|_{T}=\partial n/\partial T|_{\mu}$ on the thermodynamic quantities. Ordering the terms with respect to the partial derivatives of the effective coupling gives an elliptic quasilinear partial differential equation$$a_{T}\frac{\partial G^{2}}{\partial T}+a_{\mu}\frac{\partial G^{2}}{\partial\mu}=b,\label{eq:floweq}$$ named hereafter flow equation, with the coefficients $a_{T}$, $a_{\mu}$ and $b$ depending on $T$ and $\mu$ explicitly and, via the self-energies, implicitly. It is solved by the method of characteristics by introducing a curve parameter $x$, assuming that $T=T(x)$, $\mu=\mu(x)$ and $G^{2}=G^{2}(x)$. Subsequently, the comparison of $G_{,x}^{2}=G_{,T}^{2}T_{,x}+G_{,\mu}^{2}\mu_{,x}$ with the flow equation gives a system of three linear, coupled ordinary differential equations: $G_{,x}^{2}=-b$, $T_{,x}=-a_{T}$ and $\mu_{,x}=-a_{\mu}$ which can be solved using standard numerical methods. The initial condition for the flow equation is the effective coupling at $\mu=0$, with model parameters fixed by comparison of the entropy density with lattice results.

The effective QPM {#sec:eQP}
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Assuming that transversal gluons and quark particle excitations propagate predominantly on mass shells the full HTL QPM can be significantly simplified as it implies explicit (asymptotic) dispersion relations $\omega_{i}(k)$ of the form $\omega_{i}^{2}(k)=k^{2}+m_{i,\infty}^{2}$ as approximations to the full, implicit ones [@Pes02]. The $m_{i,\infty}$ terms depend neither on energy nor momentum and are therefore called asymptotic (thermal) masses. In order 