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The hadron resonance gas model and its extension to include the Hagedorn spectrum is discussed. The Hagedorn temperature, TH is determined from the number of hadronic resonances including all mesons and baryons. This leads to the result TH = 174 ± 11 MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We apply this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials using the chemical freeze-out curve. We compare some of our results to those obtained previously papers. Furthermore, a discussion is presented of results with identified particles at the Large Hadron Collider. Possible deviations from the standard statistical distributions are investigated by considering in detail results obtained using the Tsallis distribution. Theoretical issues are clarified concerning the thermodynamic consistency of the Tsallis distribution in the particular case of relativistic high energy quantum distributions. An improved form is proposed for describing the transverse momentum distribution and fits are presented together with estimates of the parameter q and the temperature T.
