content_image/374017.jpg content_image/374016.jpg content_image/374015.jpg
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 

<img src='content_image/374017.jpg'>

The first term on the right hand side of Eq.(119) is the discrete low-lying hadron mass spectrum 

<img src='content_image/374016.jpg'>

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: 

<img src='content_image/374015.jpg'>

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 

