of the spectrum by applying the parity properties once more gives the explicit expressions$$\begin{aligned}
s_{q/s,\text{TL}} & \!\!=\!\! & \,\,\,\,\,2d_{q/s}\int_{{\mathrm{d}^{3}k}}\int\limits _{0}^{\infty}\!\frac{{\mathrm{d}\omega}}{2\pi}\,(.)\left\{ \pi\Theta\!\left(\text{-}{\text{Re}}S_{+}^{-1}\right)-\arctan\!\left(\frac{{\text{Im}}\Sigma_{+}}{{\text{Re}}S_{+}^{\text{-}1}}\!\right)+\mbox{Re}S_{+}\mbox{Im}\Sigma_{+}\!\right\} ,\label{eq:sq TL-Pl split}\\
s_{q/s,\text{Pl}} & \!\!=\!\! & -2d_{q/s}\int_{{\mathrm{d}^{3}k}}\int\limits _{0}^{\infty}\!\frac{{\mathrm{d}\omega}}{2\pi}\,(.)\left\{ \pi\Theta\!\left(\,\,{\text{Re}}S_{-}^{-1}\right)-\arctan\!\left(\frac{{\text{Im}}\Sigma_{-}}{{\text{Re}}S_{-}^{\text{-}1}}\!\right)+\mbox{Re}S_{-}\mbox{Im}\Sigma_{-}\!\right\} ,\label{eq:sq TL-Pl split Pl}\end{aligned}$$ where the sum of the derivatives of the distribution functions is abbreviated by the parentheses $(.)$. While this separation seems straightforward, it has to be handled with care as the Landau damping term within the quark self-energies $\Sigma_{\pm}$ (see the imaginary parts in Figure \[fig:quark se\]) can, in general, not be separated into quark and plasmino contributions in this simple way.

The full HTL QPM
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Since the entropy density of the quark-gluon plasma for 2-loop QCD is the sum of the single quasiparticle entropy density contributions, it can be considered as mixture of non-interacting ideal quasiparticle gases. It is natural to assume that the pressure, which follows from the entropy density by integration, consists of single partial pressures, too. Therefore, we use the ansatz $p=p_{g,\text{T}}+p_{g,\text{L}}+\sum_{i=q,s}p_{i}-B({\Pi_\text{T}},{\Pi_\text{L}},\Sigma_{\pm})$ for the pressure, where $B$ is chosen appropriately to ensure thermodynamic consistency. The ansatz has to satisfy $s_{i}=\partial p_{i}/\partial T|_{\mu}$ which leads to$$\begin{aligned}
p_{g,\text{T}} & = & +2d_{g}\int_{{\mathrm{d}^{4}k}}{n_\text{B}}\Big\{\pi\varepsilon(\omega)\Theta\!\left(-{\text{Re}}{D_\text{T}}^{-1}\right)-\arctan\frac{{\text{Im}}{\Pi_\text{T}}}{{\text{Re}}{D_\text{T}}^{\text{-}1}}+\mbox{Re}{D_\text{T}}\mbox{Im}{\Pi_\text{T}}\Big\},\\
p_{g,\text{L}} & = & -\,\,\, d_{g}\int_{{\mathrm{d}^{4}k}}{n_\text{B}}\Big\{\pi\varepsilon(\omega)\Theta\!\left(+{\text{Re}}{D_\text{L}}^{-1}\right)-\arctan\frac{{\text{Im}}{\Pi_\text{L}}}{{\text{Re}}{D_\text{L}}^{\text{-}1}}+\mbox{Re}{D_\text{L}}\mbox{Im}{\Pi_\text{L}}\,\Big\},\\
p_{q/\! s} & = & 