We provide an update of the overview of imprints of Tsallis nonextensive
statistics seen in a multiparticle production processes. They reveal an
ubiquitous presence of power law distributions of different variables
characterized by the nonextensivity parameter q > 1. In nuclear collisions one
additionally observes a q-dependence of the multiplicity fluctuations
reflecting the finiteness of the hadronizing source. We present sum rules
connecting parameters q obtained from an analysis of different observables,
which allows us to combine different kinds of fluctuations seen in the data and
analyze an ensemble in which the energy (E), temperature (T) and multiplicity
(N) can all fluctuate. This results in a generalization of the so called
Lindhard's thermodynamic uncertainty relation. Finally, based on the example of
nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon
collisions) we demonstrate that, for the standard Tsallis entropy with degree
of nonextensivity q < 1, the corresponding standard Tsallis distribution is
described by q' = 2 - q > 1.Comment: 12 pages, 3 figures. Based on invited talk given by Z.Wlodarczyk at
SigmaPhi2011 conference, Larnaka, Cyprus, 11-15 July 2011. To be published in
Cent. Eur. J. Phys. (2011
