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Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and L\'evy distributions
High Energy Physics - Phenomenology · Submitted 25 Aug 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution.
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The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution. | result 0.94 | 0.84 | 0.92 | asserted 1.00 |
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Original abstract
The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution.
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References
How the literature uses it
24 arXiv papers cite this in 28 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 4 papers
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For each multiplicity class, the yield is extrapolated to the unmeasured region ($<0.5$ ) by fitting a Lévy-Tsallis function [ref] to the measured spectra.
Multiplicity dependence of K*(892)$^{0}$ and $\phi$(1020) production in pp collisions at $\sqrt{s}$ = 13 TeV · Results · 1.00
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The -integrated particle yields () and average transverse momenta () are calculated by integrating the measured transverse momentum spectra and using the Lévy-Tsallis parametrization [ref] to extrapolate to the low regions not covered by the measurements.
Multiplicity dependence of $\pi$, K, and p production in pp collisions at $\sqrt{s} = 13$ TeV · Results and discussion · 0.98
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To calculate the integrated yield () and the mean the spectra have been fitted with the Lévy-Tsallis function [ref] : [equation] where $m$ is the particle rest mass (i.e. the mass of the deuteron), $m_T=√(m^2+p_T^2)$ is the transverse mass, while $n$, and $C$ are free fit parameters.
(Anti-)Deuteron production in pp collisions at $\sqrt{s}=13$ TeV · Results and Discussion · 0.99
Compares with it 3 papers
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Note that the above deformed entropy differs from the usual “quantum-corrected” one with logarithmic corrections [ref] , however it resembles Tsallis nonextensive entropy [ref] , nevertheless the involved physical principles and foundations are radically different.
The generalized second law of thermodynamics with Barrow entropy · Introduction · 0.97
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The new exponent $Δ$ quantifies the quantum-gravitational deformation, and it is bounded as $0 ≤Δ≤1$, with $Δ=1$ corresponding to the most intricate and fractal structure, while $Δ=0$ corresponds to the simplest horizon structure in which case the standard Bekenstein-Hawking entropy is restored (note that the above formula is similar with Tsallis nonextensive entropy [ref] , although the physical principles and interpretation is completely different).
Modified cosmology through spacetime thermodynamics and Barrow horizon entropy · Introduction · 0.84
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Notice that the above quantum-gravitationally corrected entropy is different than the usual “quantum-corrected” entropy with logarithmic corrections [ref] , however it resembles Tsallis nonextensive entropy [ref] , nevertheless the involved foundations and physical principles are completely different.
Barrow holographic dark energy · Introduction · 0.95
Cites it as background 10 papers
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In this regard, the energy density is assumed to originate from Tsallis entropy [ref] addressed as Tsallis HDE[It was shown by Tsallis and Cirto [ref] that the entropy of a black hole should be generalized to $S = γA^δ$ where $A$ stands for the area of the black hole, $δ$ is the Tsallis parameter (or nonextensive parameter), and $γ$ is an unknown parameter.
Tsallis holographic inflation in $f(R,T)$ gravity: CMB constraints, reheating, and swampland implications · Introduction · 0.80
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Tsallis non-additive entropy [ref] generalizes the standard thermodynamics to non-extensive one, and it possess the standard Boltzmann-Gibbs statistics as a limit.
Alleviating both $H_0$ and $\sigma_8$ tensions in Tsallis cosmology · Modified cosmology through Tsallis entropy · 0.99
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In recent years a lot of attentions have arisen to the non-extensive entropy formalism, where total entropy of a system cannot necessarily obtained via summation of that of the subsystems [ref] .
Ghost Dark Energy in Tsallis and Barrow Cosmology · Introduction · 1.00
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