Nuclear matter Hagedorn Phase Quarkyonic Phase! QGP (Deconfined phase) CFL color-super conductivity non-CFL quark liquid Hadronic Phase (Vacuum) Mesonic phase Baryonic phase Strangeness More- complex-flavor- structure Color-flavor-coupling Color-neutral Colored QGP Non-singlet-state Color-singlet Temperature (T) 1 2 3 Internal color structure exponent: , B FIG. 3: (Color online) Same as Fig. (1). The order of the phase transition from the hadronic phase to the quark-gluon-plasma is shown to depend on the Hagedorn mass spectral exponent α . The exponent α is modified and increases with respect to µ$_{B}$ . The order of the phase transition is likely to be the first order, second order and higher order for the exponents α$_{1}$ , α$_{2}$ and α$_{3}$ respectively. The quark-gluon plasma is likely to maintain the color neutrality one with the higher order phase transition at small µ$_{B}$ and high T ∼ T$_{c}$ before it switches to the true deconfined colored plasma when µ$_{B}$ increases. The exponent α depends on the Hagedorn’s internal color, flavor and configuration symmetries. 68