Grzegorz Wilk, Zbigniew Wlodarczyk
In order to account for possible nonstatistical fluctuations in a hadronizing
system (leading to the characteristic power-like behavior of the respective
single particle spectra and to the broadening of the corresponding
multiparticle distributions) while using the statistical approach one has to
resort to its nonextensive version. The new parameter q appearing there is
directly connected to the variance of the particular variable X, q =
1+Var(X)/^2 (with q = 1 for the usual statistical model). We shall
demonstrate here how such an approach allows us to compose fluctuations of
different observables (described by their respective parameters q) leading to a
characteristic sum rule connecting q's deduced from measurements of these
observables, which can be verified experimentally. We shall also discuss
ensembles in which all relevant quantities, namely the energy (U), temperature
(T) and multiplicity (N), can fluctuate. A specific relation connecting all
these fluctuating variables is proposed. It generalizes the so called Lindhard
thermodynamic uncertainty relations known in the literature, by introducing, in
a natural way, a possibility of correlations between the fluctuating variables
considered. This point is illustrated using an example from the multiparticle
production processes. We show that fluctuations from different parts of phase
space (characterized by different parameters q) are correlated and that the
strength of these correlations is a function of these q's, Cov(U,T) = F({q}).
These correlations can be tested experimentally. Some rough first estimates,
using available data, are presented.
View original:
http://arxiv.org/abs/1202.2711
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