present study. In fact, there is N 2 c adjoint degrees of freedom in the U ( N$_{c}$ ) unitary represen- tation and the unimodular constraint reduces the number of degree of freedom by one. When the Hagedorn’s internal structure is mutated from the colorless unitary state to the colorless orthogonal state, the number of (Hagedorn’s internal) adjoint gluon degrees of freedom is reduced from N 2 c to N$_{c}$ ( N$_{c}$ + 1) / 2, respectively. Therefore, the N$_{c}$ ( N$_{c}$ − 1) / 2 free colorless gluons escape from the Hagedorn bag and emerge in the medium as jets. The nuclear matter turns to be dominated by the orthogonal Hagedorns and is enriched by gluonic content. The N$_{c}$ ( N$_{c}$ − 1) / 2 gluon species may glue together and probably emerge as color-neutral glueballs or jets. When the temperature T increases, the surfaces of colored bags are perturbed and expand by the thermal excitations and the system undergoes smooth phase transition to true deconfined quark-gluon plasma. The higher order phase transition is not usually asso- ciated with the explosive quark-gluon plasma. Moreover, it seems that the colored bags that emerge through smooth phase transition are rather mechanically stable. Hence the preceding scenario leads to smooth cross-over phase transition to quark-gluon plasma at µ$_{B}$ ≈ 0 and high T and on the left hand side of the tri-critical point. In the present approximation, the liberated gluons are considered as an ideal gas of massless particles. However, the breaking of the Hagedorn’s internal symmetry from the unitary symmetry to the orthogonal one may breaks the color global part of the liberated gluons and they acquire finite mass through the Higgs mechanism. This mechanism will suppress the contribution of the gluon’s partition function in particular if the liberated gluons attain large masses. 

On the other hand, when the system is compressed and cooled down, the higher order phase transition is reduced to the first order one at the moderate nuclear density. This takes place as µ$_{B}$ increases and exceeds the tri-critical point (i.e. on the right hand side of the tri-critical point). The system prefers to be dominated by the unitary Hagedorns in the stripe above the Gross-Witten point and below the quark-gluon plasma. When the medium becomes denser and hotter, the unitary Hagedorn states will not transmute to orthogonal Hagedorn states anymore but instead they become rather mechanically unstable and the system prefers to pass direct deconfinement phase transition to quark-gluon plasma. Due to the high thermal excitations, they likely pass the first order transition to quark-gluon plasma. This kind of phase transition breaks badly the color-singlet constraint and subsequently the colored SU ( N$_{c}$ ) symmetry becomes possible. Therefore, the system undergoes first order deconfinement phase transition to explosive quark-gluon plasma at moderate µ$_{B}$ = 0. Unlike 

