We derive Tsallis entropy from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem temperature, T_1 and the q parameter in terms of the temperature, T, entropy, S, and heat capacity, C of the ideal reservoir as T_1=T\exp(-S/C) and q=1-1/C. In the infinite C limit, irrespective to the value of S, the Boltzmann-Gibbs approach is fully recovered. We apply this framework for the experimental determination of the original temperature of a finite thermostat, T, from the analysis of hadron spectra produced in high energy collisions, by analyzing frequently considered simple models of the quark-gluon plasma. |