  The thermodynamical partition function for a gas of color-singlet bags
consisting of fundamental and adjoint particles in both $U(N_c)$ and $SU(N_c)$
group representations is reviewed in detail. The constituent particle species
are assumed to satisfy various thermodynamical statistics. The gas of bags is
probed to study the phase transition for a nuclear matter in the extreme
conditions. These bags are interpreted as the Hagedorn states and they are the
highly excited hadronic states which are produced below the phase transition
point to the quark-gluon plasma. The hadronic density of states has the
Gross-Witten critical point and exhibits a third order phase transition from a
hadronic phase dominated by the discrete low-lying hadronic mass spectrum
particles to another hadronic phase dominated by the continuous Hagedorn
states. The Hagedorn threshold production is found just above the highest known
experimental discrete low-lying hadronic mass spectrum. The subsequent Hagedorn
phase undergoes a first order deconfinement phase transition to an explosive
quark-gluon plasma. The role of the chiral phase transition in the phases of
the discrete low-lying mass spectrum and the continuous Hagedorn mass spectrum
is also considered. It is found crucial in the phase transition diagram.
Alternate scenarios are briefly discussed for the Hagedorn gas undergoes a
higher order phase transition through multi-processes of internal color-flavor
structure modification.
