  We derive Tsallis entropy, Sq, 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, T1, and the index q in terms of the temperature, T,
entropy, S, and heat capacity, C of the reservoir as T1 = 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.
