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 temperatu
re, 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.
Varying the proposition that acceleration itself would simulate a thermal environment, we investigate the semiclassical photon radiation as a possible telemetric thermometer of accelerated charges. Based on the classical Jackson formula we obtain the
equivalent photon intensity spectrum stemming from a constantly accelerated charge and demonstrate its resemblances to a thermal distribution for high transverse momenta. The inverse transverse slope differs from the famous Unruh temperature: it is larger by a factor of pi. We compare the resulting direct photon spectrum with experimental data for AuAu collisions at RHIC and speculate about further, analytically solvable acceleration histories.
The scaling of charged hadron fragmentation functions to the Tsallis distribution for $0.01 lessapprox x lessapprox 0.2$ is presented for various $e^+e^-$ collision energies. A possible microcanonical generalisation of the Tsallis distribution is pro
posed, which gives good agreement with measured data up to $xapprox1$. The proposal is based on superstatistics and a $KNO$ like scaling of multiplicity distributions in $e^+e^-$ experiments.
