same way. The continuous high-lying density of states ρ$_{(}$$_{II}$$_{)}$ ( T, Λ , m ) is decomposed to where summations are carried over the baryonic and strangeness quantum number B and S , respectively. The exotic Hagedorn states are assumed negligible and they are dropped from the calculations. This approximation seems to be reasonable for the hot and diluted matter. Fortunately, the situation is simpler in the case of small µ$_{B}$ and high T rather than for large µ$_{B}$ and low T . The partition functions for mesonic and baryonic Hagedorns read and respectively, where m$_{0}$ is determined from the threshold mass m$_{0}$ = m$_{th}$ . The Fermi- Dirac and Boson-Einstein ensembles for the baryonic and mesonic Hagedorns are given in Eqs.(125) and (126), respectively. For example, the mesonic and baryonic fugacities are given by Λ$_{M}$ = 1 in the case of no strange degree of freedom is included (i.e. µ$_{S}$ = 0) and Λ$_{B}$ = e µ$_{B}$$^{/T}$, respectively. The grand potential for the mesonic and baryonic Hagedorn states are calculated, respec- tively, as follow 36 Ω$_{(}$$_{II}$$_{)}$ V (Mesonic Hagedorn gas) = − T ∂ ∂ V ln Z$_{(}$$_{II}$$_{)}$ (Mesonic) , (131) ln Z$_{(}$$_{II}$$_{)}$ (Baryonic) = ln Z$_{(}$$_{II}$$_{)}$ ( T, V, Λ$_{B}$; Baryonic) , = ∫ ∞ m$_{0}$ dm ρ$_{(}$$_{II}$$_{)}$ ( T, Λ$_{B}$ , m ; Baryonic) × [ ln z$_{FD}$ ( T, m, Λ$_{B}$) + ln z$_{FD}$ ( T, m, Λ − 1 B )] , (130) ln Z$_{(}$$_{II}$$_{)}$ (Mesonic) = ln Z$_{(}$$_{II}$$_{)}$ ( T, V, Λ$_{M}$; Mesonic) , = ∫ ∞ m$_{0}$ dm ρ$_{(}$$_{II}$$_{)}$ ( T, Λ$_{M}$ , m ; Mesonic) × [ ln z$_{BE}$ ( T, m, Λ$_{M}$) + ln z$_{BE}$ ( T, m, Λ − 1 M )] , (129) ρ$_{(}$$_{II}$$_{)}$ ( T, Λ , m ) = ∑ S ρ$_{(}$$_{II}$$_{)}$ ( T, Λ$_{M}$ , m ; Mesonic) + S ρ$_{(}$$_{II}$$_{)}$ ( T, Λ$_{B}$ , m ; Baryonic) + ∑ B ∑ S ρ$_{(}$$_{II}$$_{)}$ ( T, Λ$_{Exotic}$ , m ; Exotic) , (128)