This research addresses extensive and non-extensive thermodynamics. A comparison between the entropy for both different statistics are presented. The non-extensive parameter, entropic index q, is discussed. We attempt to explore the limit of the non-extensive parameter by comparing the theoretical results with lattice and the available experimental results. The two thermal parameters T, B are calculated with the freeze-out condition S/T^3 = 7 for different q. The motivation of this research comes from recent non-extensive statistics studies which showed that this standard thermodynamics failed to reproduce the freeze-out parameters. As an application, the black-hole entropy is calculated in the quantum Generalized Uncertainty Principle (GUP) modification form. Black-hole entropy may reveal information about the thermodynamics it belongs. This discrimination is essential to quantify the entropy in the hadron production evolution stage and in the black-hole thermodynamics. It is concluded that lattice QCD reproduces the extensive thermodynamics very well. Also, the black hole appears as an extensive system.