  Relativistic particle production often requires the use of Tsallis statistics
to account for the apparently power-like behavior of transverse momenta
observed in the data even at a few GeV/c. In such an approach this behavior is
attributed to some specific intrinsic fluctuations of the temperature $T$ in
the hadronizing system and is fully accounted by the nonextensivity parameter
$q$. On the other hand, it was recently shown that similar power-law spectra
can also be obtained by introducing some specific volume fluctuations,
apparently without invoking the introduction of Tsallis statistics. We
demonstrate that, in fact, when the total energy is kept constant, these volume
fluctuations are equivalent to temperature fluctuations and can be derived from
them. In addition, we show that fluctuations leading to multiparticle power-law
Tsallis distributions introduce specific correlations between the considered
particles. We then propose a possible way to distinguish the fluctuations in
each event from those occurring from event-to-event. This could have
applications in the analysis of high density events at LHC (and especially in
ALICE).
