Fractal Structures of Yang–Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics

Deppman, A.; Megías, Eugenio; Menezes, D. P.

doi:10.3390/physics2030026

Cited by 31 publications

(23 citation statements)

References 100 publications

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“…We have also investigated the structure of a thermodynamical system presenting fractal properties, showing that it naturally leads to Tsallis non-extensive statistics. Based on the self-similar properties of thermofractals, we have explained how a field theoretical approach for thermofractals can account for the dynamics of effective partons, and correctly reproduces the beta function of QCD, leading to a value of the entropic index q 1.14 which turns out to be in excellent agreement with phenomenological analyses [19,20,51].…”

Section: Discussionmentioning

confidence: 72%

“…There are still many open questions. Regarding the description of HEP data by power-law distributions, the main problem is to verify to what extent the idea of fractal structure can describe experimental data, including analyses of the fractal dimension that can be accessed through intermittency analysis [52,51]. These analyses can be eventually extended also for heavy-ion collisions [53].…”

Section: Discussionmentioning

confidence: 99%

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Tsallis statistics and thermofractals: applications to high energy and hadron physics

Megías¹,

Andrade-II²,

Deppman³

et al. 2022

Preprint

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We study the applications of non-extensive Tsallis statistics to high energy and hadron physics. These applications include studies of pp collisions, equation of state of QCD, as well as Bose-Einstein condensation. We also analyze the connections of Tsallis statistics with thermofractals, and address some of the conceptual aspects of the fractal approach, which are expressed in terms of the renormalization group equation and the self-energy corrections to the parton mass. We associate these wellknown concepts with the origins of the fractal structure in the quantum field theory.

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Section: Discussionmentioning

confidence: 72%

Section: Discussionmentioning

confidence: 99%

Tsallis statistics and thermofractals: applications to high energy and hadron physics

Megías¹,

Andrade-II²,

Deppman³

et al. 2022

Preprint

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“…That conclusion can be applied to fractal networks as those studied in the present work. Remarkably, renormalization seems to be an essential feature in thermofractals [ 21 , 38 ], Yang-Mills fields [ 25 ] (see [ 39 ] for a review on the subject) and in fractal networks [ 19 ]. The possibility of finding a common theoretical framework joining fractal networks and Tsallis statistics is an interesting subject of research.…”

Section: Introductionmentioning

confidence: 99%

Emergency of Tsallis statistics in fractal networks

Deppman

Andrade-II

2021

PLoS ONE

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Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

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“…The generalized entropy leads to a non-extensive thermodynamics that reduces to the standard Boltzmann-Gibbs theory when the entropic parameter, q, approaches the unit [6]. Although the reasons for the large number of systems following the Tsallis statistics are not yet clear, a recent result on the mechanism for the emergence of the non-additive entropy can give some clues on the subject [7,8].…”

Section: Introductionmentioning

confidence: 99%

Bose-Einstein condensation and non-extensive statistics

Megias,

Timóteo,

Gammal

et al. 2021

Preprint

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We study the Bose-Einstein condensation in non-extensive statistics for a free gas of bosons, and extend the results to the non-relativistic case as well. We present results for the dependence of the critical temperature and the condensate fraction on the entropic index, q, and show that the condensate can exist only for a limited range of q in both relativistic and non-relativistic systems. We provide numerical results for other thermodynamics quantities like the internal energy, specific heat and number fluctuations. We discuss the implications for high energy physics and hadron physics. The results for the non-relativistic case can be of interest in coldatom systems.

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Fractal Structures of Yang–Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics

Cited by 31 publications

References 100 publications

Tsallis statistics and thermofractals: applications to high energy and hadron physics

Tsallis statistics and thermofractals: applications to high energy and hadron physics

Emergency of Tsallis statistics in fractal networks

Bose-Einstein condensation and non-extensive statistics

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