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Correlations from generalized thermodynamics

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)/<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&#39;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&#39;s, Cov(U,T) = F({q}). These correlations can be tested experimentally. Some rough first estimates, using available data, are presented.