What thermodynamics tells us about the QCD plasma

As long as a rapid change of the entropy density $s\left(T\right)\mathrm{}$ takes place across the critical temperature $T_c$ of the QCD phase transition, the pressure $P\left(T\right),$ and the energy density $e\left(T\right)\mathrm{}$ normalized by their Stefan-Boltzmann values generally deviate from unity for $T\gg T_c,$ even if there are no interactions among quarks and gluons at $T>\mathrm{}{T}_c.$ We shall demonstrate this both analytically and numerically for a general class of $s\left(T\right)\mathrm{}$ consistent with thermodynamical constraints and make a qualitative comparison of the result with the lattice QCD data. Quantities related to $\mathrm{ds}\left(T\right)/dT$ such as the specific heat and sound velocity are also discussed.