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The thermodynamical partition function for a gas of color-singlet bagsconsisting of fundamental and adjoint particles in both $U(N_c)$ and $SU(N_c)$group representations is reviewed in detail. The constituent particle speciesare assumed to satisfy various thermodynamical statistics. The gas of bags isprobed to study the phase transition for a nuclear matter in the extremeconditions. These bags are interpreted as the Hagedorn states and they are thehighly excited hadronic states which are produced below the phase transitionpoint to the quark-gluon plasma. The hadronic density of states has theGross-Witten critical point and exhibits a third order phase transition from ahadronic phase dominated by the discrete low-lying hadronic mass spectrumparticles to another hadronic phase dominated by the continuous Hagedornstates. The Hagedorn threshold production is found just above the highest knownexperimental discrete low-lying hadronic mass spectrum. The subsequent Hagedornphase undergoes a first order deconfinement phase transition to an explosivequark-gluon plasma. The role of the chiral phase transition in the phases ofthe discrete low-lying mass spectrum and the continuous Hagedorn mass spectrumis also considered. It is found crucial in the phase transition diagram.Alternate scenarios are briefly discussed for the Hagedorn gas undergoes ahigher order phase transition through multi-processes of internal color-flavorstructure modification.

The thermodynamics for a hadronic gas of fireballs with internal color structures and chiral fields