What thermodynamics tells us about the QCD plasma

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