quark-gluon bags (or quark-gluon liquid). Furthermore, the color-singlet states for the quark bag with U (1) N$_{c}$ color symmetry group can be argued to be quark rich liquid bags and gluon rich medium. The phase transition to the colorless orthogonal states (i.e. orthogonal Hagedorns) or colorless U (1) N$_{c}$ states may explain the fluid properties and the low viscosity factor for the quark-gluon plasma at the RHIC and possibly LHC. This class of phase transition enriches the medium with gluonic jets besides the Hagedorn states. Furthermore, in the case that the orthogonal or U (1) N$_{c}$ Hagedorn states freeze out at some point before reaching the quark-gluon plasma, they evaporate to the (exotic-) low-lying mass spectrum particles via Gross-Witten like phase transition in an analogous way to the black holes evaporation in AdS/CFT. 

The hot and little compressed hadronic matter ( µ$_{B}$ ̸ = 0) is likely to be dominated by the orthogonal Hagedorn states above the Gross-Witten point. This kind of nuclear matter tends to undergo higher order phase transition ( for instance third order with α =3 ) to the deconfined quark-gluon plasma. In this case, the color-singlet state of the orthogonal symmetry group is broken smoothly to form the colored SU ( N$_{c}$ ) state (i.e. color-non-singlet state) and, subsequently, the quarks and gluons are liberated. At the intermediate baryonic chemical potential µ$_{B}$ , the continuous high-lying unitary Hagedorn matter undergoes first order phase transition to explosive quark-gluon plasma. The color-singlet state is broken badly to form the colored SU ( N$_{c}$ ) state. The explosive quark-gluon plasma needs much thermal energy to be detonated. Furthermore, it should be noted that when µ$_{B}$ is reduced below a critical value, the unitary Hagedorn states tend to transmute to the orthogonal Hagedorn states prior to the deconfinement phase transition to quark-gluon plasma but this is not the case for the saturate orthogonal Hagedorn matter when µ$_{B}$ increases and exceeds a critical value. 

On the other hand, the mass spectral exponents for the unitary and symplectic Hagedorn states are reduced to α$_{2}$ = 9 / 2 and α$_{3}$ = 15 / 2. This means that the nuclear matter which is dominated by the unitary Hagedorn states likely undergoes direct first order phase transition to the quark-gluon plasma. Furthermore, it is obvious that the symplectic nuclear matter likely undergoes first order phase transition to the explosive quark-gluon plasma when it is heat up. 

When the hadronic matter is compressed to the significantly large m$_{B}$ and cooled down, the unitary Hagedorn states are mutated to the symplectic ones due to the internal color- 

