and In order to simplify the treatment, we follow the standard procedure for heavy Hagedorn states ( m$_{0}$ > 2 GeV) those dominates the dilute and hot nuclear matter. The partition functions for classical mesonic and baryonic Hagedorn states, respectively, read and The exotic Hagedorn states with the baryonic number B > 1 are assumed to be suppressed and subsequently they are dropped from the calculations. The classical statistics is an adequate approximation for the flavor invariance when the dilute nuclear matter is heated. However, in the case of the cold and highly compressed nuclear matter, the classical Maxwell- Boltzmann statistic fails for the mesonic Hagedorn states when the meson condensation (in particular the strangeness) takes place in the system. Hence, the exact quantum Bose- Einstein and Fermi-Dirac statistics become essential for cold and dense nuclear matter. The high-lying strangeness condensation takes place when the mesonic Hagedorn frequency approaches zero. This phenomenon takes place when the strange chemical potential µ$_{S}$ reaches a critical value. Hence, under such a circumstance, the Bose-Einstein statistics must be taken exactly in the calculation. Furthermore, the exotic Hagedorn states may turn to be important when the nuclear matter becomes extremely dense in order to soften the equation of state. Fortunately, in the neighborhood of the tri-critical point, the condensation is not expected in the hot and dilute nuclear matter and the classical Maxwell-Boltzmann statistics 37 ln z$_{FD}$ ( T, m, Λ$_{B}$) = (2 J$_{B}$ + 1) V ∫ d $^{3}$k (2 π ) 3 ln ( 1 + Λ$_{B}$ e − √ ( k $^{2}$+ m $^{2}$) /T ) , ≈ (2 J$_{B}$ + 1)Λ$_{B}$ V ∫ d $^{3}$k (2 π ) $_{3}$e − √ ( k $^{2}$+ m $^{2}$) $^{/T}$, ≈ (2 J$_{B}$ + 1)Λ$_{B}$ V ( mT 2 π ) 3 / 2 e − $^{m/T}$. (134) ln z$_{BE}$ ( T, m, Λ$_{M}$) = − (2 J$_{M}$ + 1) V ∫ d $^{3}$k (2 π ) 3 ln ( 1 − Λ$_{M}$ e − √ ( k $^{2}$+ m $^{2}$) /T ) , ≈ (2 J$_{M}$ + 1)Λ$_{M}$ V ∫ d $^{3}$k (2 π ) $_{3}$e − √ ( k $^{2}$+ m $^{2}$) $^{/T}$, ≈ (2 J$_{M}$ + 1)Λ$_{M}$ V ( mT 2 π ) 3 / 2 e − $^{m/T}$, (133) Ω$_{(}$$_{II}$$_{)}$ V (Baryonic Hagedorn gas) = − T ∂ ∂ V ln Z$_{(}$$_{II}$$_{)}$ (Baryonic) . (132)