rich and the multiple intermediate transition processes are found essential. The nuclear matter which is dominated by the unitary Hagedorn states passes different phase transitions with different orders depending on the nuclear medium’s temperature and density. The dilute nuclear matter that is enriched with the unitary Hagedorn states undergoes phase transition to another matter that is dominated by the orthogonal Hagedorn states when the medium is heated up while the extreme dense nuclear matter that is dominated by the unitary Hagedorn states passes phase transition to another one that is dominated by the symplectic Hagedorn states when the medium is further compressed and cooled down. It should be noted that the Hagedorn states are colorless (by projecting only the color-singlet states) regardless of their internal symmetry group. Furthermore, it is possible to imagine under the assumption of certain scenarios that the Hagedorn states passes smooth multiple phase transitions to a neutral color gas of metastable colored bags at T ≈ T$_{c}$ and µ$_{B}$ ≈ 0. The tri-critical point in the µ$_{B}$ − T phase transition diagram and the fluid behaviour of the quark-gluon plasma at a low baryonic chemical potential µ$_{B}$ and high temperature T ≫ 0 can be interpreted in terms of the modification of the Hagedorn mass spectral density due to the modification in the quark-gluon bag’s internal symmetry. At low temperature, the nuclear matter is dominated by the discrete low-lying mass spectrum (hadrons) and when the system is heated up it undergoes higher order phase transition to new nuclear matter that is dominated by the continuous high-lying mass spectrum particles (i.e. Hagedorns). When the Hagedorn states freeze out they evaporate to the discrete low-lying particles through Gross-Witten phase transition in an analogous way to the fragmentation of the big soap bubble to many tiny bubbles. The Hagedorn states are determined basically by the mass spectrum of the quark and gluon bag with a specific internal symmetry. The color-singlet constraint which guarantees the colorless quark-gluon bags plays an essential role in keeping quarks and gluons confined. The continuous high-lying hadronic matter is dominated at first by the unitary Hagedorn states just above the Gross-Witten point (it appears as a line in µ$_{B}$ − T plane) for the phase transition from the discrete low-lying hadronic matter to the continuous high-lying one. The mass spectral exponent α of the continuous high-lying mass spectral density ρ$_{(}$$_{II}$$_{)}$ ( m ) = c m − $^{α}$ebm depends on the underlying internal symmetry of the Hagedorn bag. The composite bag’s internal symmetry is modified from the colorless unitary state to the colorless orthogonal state in the RHIC and/or LHC energy at high temperature. On the 57