where the index i run over the unimodular-like orthogonal O$_{S}$ ( N$_{c}$ ), unitary U ( N$_{c}$ ), symplec- tic Sp ( N$_{c}$ ) and U (1) N$_{c}$ Hagedorn states, respectively. The hadronic matter consists all the known discrete low-lying mass spectrum particles those are found in the data book [3] and the continuous high-lying mass spectrum for the Hagedorn states with various internal structures. For instance the the data book [3] consists of 76 non-strange mesons and 64 non-strange baryons besides strange and other flavor hadrons. The density of states can be written as follows The first term on the right hand side of Eq.(119) is the discrete low-lying hadron mass spectrum where m$_{M}$ and Λ$_{M}$, respectively, are the meson’s mass and fugacity and m$_{B}$ and Λ$_{B}$, respec- tively, are the baryon’s mass and fugacity while m$_{E}$ and Λ$_{E}$, respectively, are exotic parti- cle’s mass and fugacity. The baryon and meson mass spectra are satisfying the Fermi-Dirac and Bose-Einstein statistics, respectively. The exotic particle satisfies either Fermi-Dirac or Bose-Einstein statistics depends on the number of its constituent quarks and antiquarks. Since the discrete low-lying mass spectrum is limited for a relatively light hadron mass m ≤ m$_{critical}$ ≈ 2 GeV for non-strange hadrons, the Fermi-Dirac and Bose-Einstein are distinctive and they are taken exactly: where the subscript notation, namely, ( Stats ) indicates either Fermi-Dirac or Bose-Einstein statistics for baryons or mesons, respectively. The low-lying mass spectrum ensemble is 33 I = Z$_{(}$$_{I}$$_{)}$ ( T, V ; Λ) , = exp (∫ m$_{0}$ 0 dm ρ$_{(}$$_{I}$$_{)}$ ( T, Λ , m ) [ ln z$_{(}$$_{Stats}$$_{)}$ ( T, m, Λ) + ln z$_{(}$$_{Stats}$$_{)}$ ( T, m, Λ − 1 )] ) , = Z$_{(}$$_{I}$$_{)}$ ( T, V ; Λ , Mesons) × Z$_{(}$$_{I}$$_{)}$ ( T, V ; Λ , Baryons) × Z$_{(}$$_{I}$$_{)}$ ( T, V ; Λ , Exotics) , (121) ρ$_{(}$$_{I}$$_{)}$ ( T, Λ , m ) = mesons ∑ M δ ( m − m$_{M}$ ) δ (Λ − Λ$_{M}$) + baryons ∑ B δ ( m − m$_{B}$ ) δ (Λ − Λ$_{B}$) + exotic ∑ E δ ( m − m$_{E}$ ) δ (Λ − Λ$_{E}$) (120) ρ ( T, Λ , m ) = ρ$_{(}$$_{I}$$_{)}$ ( T, Λ , m ) + ρ$_{(}$$_{II}$$_{)}$ ( T, Λ , m ) . (119)