the Fermi-Dirac or Bose-Einstein Statistics. These Hagedorn states are assumed to obey the classical Maxwell-Boltzmann statistics for the simplicity due to their relatively large masses. Nonetheless, in any realistic physical situation, the Hagedorn states violate the fla- vor invariance and this violation becomes negligible when the medium tends to be extreme hot and the chiral symmetry tends to be restored (i.e. the is no sufficient time for the fla- vor violation). Furthermore, the Maxwell-Boltzmann statistics is not adequate one for the highly compressed the cold (or slight warm T ≈ few tens MeV) nuclear matter. In the case of highly compressed nuclear matter where µ$_{B}$ becomes large and T is small, the quantum statistics such as Fermi-Dirac or Bose-Einstein Statistics becomes important. It is remark- able to note that the Bose-Einstein statistics is likely to lead to the Hagedorn condensation when the baryon chemical potential µ$_{B}$ becomes very large at relatively low temperature T . In this sense the quantum statistics turns to be important. The grand canonical partition function for the Hagedorn states is given by The continuous high-lying mass spectrum can be decomposed to mesonic ( B = 0) and baryonic ( B = 1) Hagedorn states and the exotic Hagedorn states with baryonic quantum number B > 1. The mesonic and baryonic fugacities are given by Λ$_{M}$ = e ( S µ$_{S}$ ) /T and Λ$_{B}$ = e ( B µ$_{B}$ + S µ$_{S}$ ) $^{/T}$, respectively, where S is the strangeness quantum number and B is the baryonic number. The (ordinary-) baryonic Hagedorns carries B = 1. The Exotic Hage- dorn’s states can carry various baryonic and strangeness quantum number B = 0 , 1 , 2 · · · etc and S = 0 , − 1 , · · · etc where the fugacity is reduced to Λ$_{Exotic}$ = e ( B µ$_{B}$ + S µ$_{S}$ ) $^{/T}$. In the case of no strangeness degree of freedom, the strangeness quantum number is reduced to S = 0. The other flavor degrees of freedom such as charmonium can be introduced in the 35 I = Z$_{(}$$_{II}$$_{)}$ ( T, V, Λ) , = exp (∫ ∞ m$_{0}$ dm ρ$_{(}$$_{II}$$_{)}$ ( T, Λ , m ) [ ln z$_{(}$$_{Stats}$$_{)}$ ( T, m, Λ) + ln z$_{(}$$_{Stats}$$_{)}$ ( T, m, Λ − 1 )] ) , = Z$_{(}$$_{II}$$_{)}$ ( T, V, Λ; Mesonic) × Z$_{(}$$_{II}$$_{)}$ ( T, V, Λ; Baryonic) × Z$_{(}$$_{II}$$_{)}$ ( T, V, Λ; Exotic) × ( · · · ) . (127)