Much experimental and theoretical effort has been devoted in the past to study the transition between quark matter and hadronic gas in ultrarelativistic nucleus-nucleus collisions (≥10 AGeV). How does the equation of state (EoS) reflect the transition from the hadronic matter to the quark-gluon-plasma (QGP)? A first-order phase transition is generically associated with the presence of a 'softest point' in the EoS. The pressure increases less than the energy density close to the critical temperature, because only the energy density 'jumps'. Quantum chromodynamics (QCD) calculations on lattices show indeed a softening of the EoS at temperatures in the transition region between pion gas and QGP. It is not yet settled whether QCD at finite temperature exhibits a true phase transition or just a rapid cross-over between the two phases. On the hadronic side, the softening is expected from the many resonance degrees of freedom which are getting populated at temperatures ≥ 140 MeV (resonance matter).
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