Interpretation of the Nonextensivity Parameterqin Some Applications of Tsallis Statistics and Lévy Distributions

Abstract

The nonextensivity parameter q occurring in some of the applications of Tsallis statistics (known also as index of the corresponding Levy distribution) is shown to be given, in the q>1 case, entirely by the fluctuations of the parameters of the usual exponential distribution.

Measurement of neutral mesons inp+pcollisions ats=200 GeVand scaling properties of hadron production

“…It is shown below that the magnitudes of T found in this work are close to T kfo extracted in the blast-wave model approach [8,71] applied to p + p data. In applications to p + p collisions it has been shown [25] that the parameter q of the Tsallis distribution of Eq. 5 can be related to the amount of temperature fluctuations in the system as:…”

“…The spectral shapes of all hadrons produced in p + p collisions at √ s =200 GeV are well described by one single distribution without making a distinct division into two regions. The Tsallis [24] distribution, also referred to as a Levy distribution [7,25], has only two parameters, T and n, that characterize the low-and high-p T regions of the spectra, respectively. This distribution has been shown by Tsallis to result from a postulated generalization of the Boltzmann-Gibbs entropy.…”

Superstatistics, thermodynamics, and fluctuations

“…The concept of superstatistics has been introduced by two of the present authors [1] after some preliminary considerations in [2,3]. The stationary distributions of superstatistical systems typically exhibit a non-Gaussian behavior with fat tails, which can decay, e.g., as a power law, a stretched-exponential law, or in an even more complicated way [4].…”

On superstatistical multiplicative-noise processes

“…In addition, superstatistical systems present a parameter,β, that fluctuates on a large scale, T , and follows a time-independent distribution, p(β). The superstatistical framework has successfully been applied on a widespread of problems like: interactions between hadrons from cosmic rays [4], fluid turbulence [3,5,6], granular material [7], electronics [8], economics [9][10][11][12], among many others [13]. Furthermore, it has been regarded as a possible foundation for non-extensive statistical mechanics [3] based on Tsallis entropy [14] as we show later on.…”