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Auteur : Grafiati
Publié le 14 mars 2023

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1

Nakamichi, A., I. Joichi, O. Iguchi et M. Morikawa. « Non-extensive galaxy distributions – Tsallis statistical mechanics ». Chaos, Solitons & ; Fractals 13, no 3 (mars 2002) : 595–601. http://dx.doi.org/10.1016/s0960-0779(01)00042-x.

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2

Shivamoggi, B. K. « Non-extensive statistical mechanics of compressible turbulence ». Physica A : Statistical Mechanics and its Applications 318, no 3-4 (février 2003) : 358–70. http://dx.doi.org/10.1016/s0378-4371(02)01368-7.

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3

Ruseckas, Julius. « Canonical ensemble in non-extensive statistical mechanics ». Physica A : Statistical Mechanics and its Applications 447 (avril 2016) : 85–99. http://dx.doi.org/10.1016/j.physa.2015.12.011.

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4

Liu, Limin, Lin Zhang et Shiqi Fan. « Optimal investment problem under non-extensive statistical mechanics ». Computers & ; Mathematics with Applications 75, no 10 (mai 2018) : 3549–57. http://dx.doi.org/10.1016/j.camwa.2018.02.016.

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5

Hansen, Steen H., Daniel Egli, Lukas Hollenstein et Christoph Salzmann. « Dark matter distribution function from non-extensive statistical mechanics ». New Astronomy 10, no 5 (avril 2005) : 379–84. http://dx.doi.org/10.1016/j.newast.2005.01.005.

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6

Gross, D. H. E. « Micro-canonical statistical mechanics of some non-extensive systems☆ ». Chaos, Solitons & ; Fractals 13, no 3 (mars 2002) : 417–30. http://dx.doi.org/10.1016/s0960-0779(01)00023-6.

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7

Vakili-Nezhaad, G. R., et G. A. Mansoori. « An Application of Non-Extensive Statistical Mechanics to Nanosystems ». Journal of Computational and Theoretical Nanoscience 1, no 2 (1 septembre 2004) : 227–29. http://dx.doi.org/10.1166/jctn.2004.021.

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8

Plastino, A. R., et A. Plastino. « Non-extensive statistical mechanics and generalized Fokker-Planck equation ». Physica A : Statistical Mechanics and its Applications 222, no 1-4 (décembre 1995) : 347–54. http://dx.doi.org/10.1016/0378-4371(95)00211-1.

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9

Bin Yang, Heling Li, Yan Ma et Ying Xiong. « Study on Traditional Extensive Statistical Mechanics in Non-extension System ». Journal of Convergence Information Technology 8, no 8 (30 avril 2013) : 906–13. http://dx.doi.org/10.4156/jcit.vol8.issue8.107.

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10

Abe, Sumiyoshi. « Conceptual difficulties with theq-averages in non-extensive statistical mechanics ». Journal of Physics : Conference Series 394 (29 novembre 2012) : 012003. http://dx.doi.org/10.1088/1742-6596/394/1/012003.

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11

Beck, Christian. « Non-extensive statistical mechanics approach to fully developed hydrodynamic turbulence ». Chaos, Solitons & ; Fractals 13, no 3 (mars 2002) : 499–506. http://dx.doi.org/10.1016/s0960-0779(01)00032-7.

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12

Beck, Christian. « Non-extensive statistical mechanics and particle spectra in elementary interactions ». Physica A : Statistical Mechanics and its Applications 286, no 1-2 (octobre 2000) : 164–80. http://dx.doi.org/10.1016/s0378-4371(00)00354-x.

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13

Okamura, Keisuke. « Affinity-based extension of non-extensive entropy and statistical mechanics ». Physica A : Statistical Mechanics and its Applications 557 (novembre 2020) : 124849. http://dx.doi.org/10.1016/j.physa.2020.124849.

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14

Ruseckas, Julius. « Canonical ensemble in non-extensive statistical mechanics, q>1 ». Physica A : Statistical Mechanics and its Applications 458 (septembre 2016) : 210–18. http://dx.doi.org/10.1016/j.physa.2016.04.020.

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15

Yang, Bin, He Ling Li et Ying Xiong. « Study on Extensive Statistical Mechanics by Nonextensivity ». Applied Mechanics and Materials 312 (février 2013) : 220–25. http://dx.doi.org/10.4028/www.scientific.net/amm.312.220.

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This paper proposes a phase rule for non-extensive systems and asserts that the thermodynamic limit commonly used in extensive statistical mechanics is no longer applicable when considering non-extensive quantities. In addition, this paper revises some of the concepts and conclusions arising in extensive statistical mechanics.
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16

Karakatsanis, L. P., A. C. Iliopoulos, E. G. Pavlos et G. P. Pavlos. « Statistical analysis of Geopotential Height (GH) timeseries based on Tsallis non-extensive statistical mechanics ». Physica A : Statistical Mechanics and its Applications 492 (février 2018) : 715–23. http://dx.doi.org/10.1016/j.physa.2017.10.051.

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17

Van Xuan, Le, Nguyen Tri Lan et Nguyen Ai Viet. « On application of non—extensive statistical mechanics to studying ecological diversity ». Journal of Physics : Conference Series 726 (juin 2016) : 012024. http://dx.doi.org/10.1088/1742-6596/726/1/012024.

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18

Ausloos, M., et F. Petroni. « Tsallis non-extensive statistical mechanics of El Niño southern oscillation index ». Physica A : Statistical Mechanics and its Applications 373 (janvier 2007) : 721–36. http://dx.doi.org/10.1016/j.physa.2006.05.044.

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19

Alberico, W. M., P. Czerski, A. Lavagno, M. Nardi et V. Somá. « Signals of non-extensive statistical mechanics in high energy nuclear collisions ». Physica A : Statistical Mechanics and its Applications 387, no 2-3 (janvier 2008) : 467–75. http://dx.doi.org/10.1016/j.physa.2007.09.005.

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20

Zhao, Pan, et Qingxian Xiao. « Portfolio selection problem with liquidity constraints under non-extensive statistical mechanics ». Chaos, Solitons & ; Fractals 82 (janvier 2016) : 5–10. http://dx.doi.org/10.1016/j.chaos.2015.10.026.

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21

Majhi, Abhishek. « Non-extensive statistical mechanics and black hole entropy from quantum geometry ». Physics Letters B 775 (décembre 2017) : 32–36. http://dx.doi.org/10.1016/j.physletb.2017.10.043.

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22

Vallianatos, Filippos. « A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution ». Geosciences 8, no 2 (5 février 2018) : 52. http://dx.doi.org/10.3390/geosciences8020052.

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23

Liu, Limin, et Yingying Cui. « European Option Based on Least-Squares Method under Non-Extensive Statistical Mechanics ». Entropy 21, no 10 (25 septembre 2019) : 933. http://dx.doi.org/10.3390/e21100933.

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This paper is devoted to the study of the pricing of European options under a non-Gaussian model. This model follows a non-extensive statistical mechanics which can better describe the fractal characteristics of price movement in the financial market. Moreover, we present a simple but precise least-square method for approximation and obtain a closed-form solution of the price of European options. The advantages of this technique are illustrated by numerical simulation, which shows that the least-squares method is better compared with Borland’s two methods in 2002 and 2004.
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24

Akıllı, Mahmut, Nazmi Yılmaz et K. Gediz Akdeniz. « The ‘wavelet’ entropic index q of non-extensive statistical mechanics and superstatistics ». Chaos, Solitons & ; Fractals 150 (septembre 2021) : 111094. http://dx.doi.org/10.1016/j.chaos.2021.111094.

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25

Duarte Queirós, Sı́lvio M. « On the connection between ARCH time series and non-extensive statistical mechanics ». Physica A : Statistical Mechanics and its Applications 344, no 3-4 (décembre 2004) : 619–25. http://dx.doi.org/10.1016/j.physa.2004.06.041.

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26

Kononovicius, A., et J. Ruseckas. « Stochastic dynamics of N correlated binary variables and non-extensive statistical mechanics ». Physics Letters A 380, no 18-19 (avril 2016) : 1582–88. http://dx.doi.org/10.1016/j.physleta.2016.03.006.

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27

Zhao, Pan, Jixia Wang et Yu Song. « Optimal Portfolio under Non-Extensive Statistical Mechanics and Value-at-Risk Constraints ». Acta Physica Polonica A 133, no 5 (mai 2018) : 1170–73. http://dx.doi.org/10.12693/aphyspola.133.1170.

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28

Zhao, Pan, et Qingxian Xiao. « Portfolio selection problem with Value-at-Risk constraints under non-extensive statistical mechanics ». Journal of Computational and Applied Mathematics 298 (mai 2016) : 64–71. http://dx.doi.org/10.1016/j.cam.2015.12.008.

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29

Ruseckas, J. « Probabilistic model of N correlated binary random variables and non-extensive statistical mechanics ». Physics Letters A 379, no 7 (mars 2015) : 654–59. http://dx.doi.org/10.1016/j.physleta.2014.12.038.

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30

Zhao, Pan, Jian Pan, Benda Zhou, Jixia Wang et Yu Song. « Hedging for the Regime-Switching Price Model Based on Non-Extensive Statistical Mechanics ». Entropy 20, no 4 (3 avril 2018) : 248. http://dx.doi.org/10.3390/e20040248.

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31

Loukidis, Andronikos, Dimos Triantis et Ilias Stavrakas. « Non-Extensive Statistical Analysis of Acoustic Emissions Recorded in Marble and Cement Mortar Specimens Under Mechanical Load Until Fracture ». Entropy 22, no 10 (2 octobre 2020) : 1115. http://dx.doi.org/10.3390/e22101115.

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Non-extensive statistical mechanics (NESM), which is a generalization of the traditional Boltzmann-Gibbs statistics, constitutes a theoretical and analytical tool for investigating the irreversible damage evolution processes and fracture mechanisms occurring when materials are subjected to mechanical loading. In this study, NESM is used for the analysis of the acoustic emission (AE) events recorded when marble and cement mortar specimens were subjected to mechanical loading until fracture. In total, AE data originating from four distinct loading protocols are presented. The cumulative distribution of inter-event times (time interval between two consecutive AE events) and the inter-event distances (three-dimensional Euclidian distance between the centers of successive AE events) were examined under the above concept and it was found that NESM is suitable to detect criticality under the terms of mechanical status of a material. This was conducted by evaluating the fitting results of the q-exponential function and the corresponding q-indices of Tsallis entropy qδτ and qδr, along with the parameters τδτ and dδr. Results support that qδτ+qδr≈2 for AE data recorded from marble and cement mortar specimens of this work, which is in good agreement with the conjecture previously found in seismological data and AE data recorded from Basalt specimens.
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32

Strzałka, D. « Non-Extensive Statistical Mechanics - a Possible Basis for Modelling Processes in Computer Memory System ». Acta Physica Polonica A 117, no 4 (avril 2010) : 652–57. http://dx.doi.org/10.12693/aphyspola.117.652.

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33

Shivamoggi, Bhimsen K., et Christian Beck. « A note on the application of non-extensive statistical mechanics to fully developed turbulence ». Journal of Physics A : Mathematical and General 34, no 19 (2 mai 2001) : 4003–7. http://dx.doi.org/10.1088/0305-4470/34/19/304.

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34

STRZAŁKA, DOMINIK, et FRANCISZEK GRABOWSKI. « TOWARDS POSSIBLE NON-EXTENSIVE THERMODYNAMICS OF ALGORITHMIC PROCESSING — STATISTICAL MECHANICS OF INSERTION SORT ALGORITHM ». International Journal of Modern Physics C 19, no 09 (septembre 2008) : 1443–58. http://dx.doi.org/10.1142/s0129183108013011.

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Tsallis entropy introduced in 1988 is considered to have obtained new possibilities to construct generalized thermodynamical basis for statistical physics expanding classical Boltzmann–Gibbs thermodynamics for nonequilibrium states. During the last two decades this q-generalized theory has been successfully applied to considerable amount of physically interesting complex phenomena. The authors would like to present a new view on the problem of algorithms computational complexity analysis by the example of the possible thermodynamical basis of the sorting process and its dynamical behavior. A classical approach to the analysis of the amount of resources needed for algorithmic computation is based on the assumption that the contact between the algorithm and the input data stream is a simple system, because only the worst-case time complexity is considered to minimize the dependency on specific instances. Meanwhile the article shows that this process can be governed by long-range dependencies with thermodynamical basis expressed by the specific shapes of probability distributions. The classical approach does not allow to describe all properties of processes (especially the dynamical behavior of algorithms) that can appear during the computer algorithmic processing even if one takes into account the average case analysis in computational complexity. The importance of this problem is still neglected especially if one realizes two important things. The first one: nowadays computer systems work also in an interactive mode and for better understanding of its possible behavior one needs a proper thermodynamical basis. The second one: computers from mathematical point of view are Turing machines but in reality they have physical implementations that need energy for processing and the problem of entropy production appears. That is why the thermodynamical analysis of the possible behavior of the simple insertion sort algorithm will be given here.
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35

Queirós, Silvio M. Duarte. « On anomalous distributions in intra-day financial time series and non-extensive statistical mechanics ». Physica A : Statistical Mechanics and its Applications 344, no 1-2 (décembre 2004) : 279–83. http://dx.doi.org/10.1016/j.physa.2004.06.132.

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36

Loukidis, Andronikos, Ilias Stavrakas et Dimos Triantis. « Non-Extensive Statistical Mechanics in Acoustic Emissions : Detection of Upcoming Fracture in Rock Materials ». Applied Sciences 13, no 5 (3 mars 2023) : 3249. http://dx.doi.org/10.3390/app13053249.

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Acoustic emission (AE), recorded during uniaxial compressive loading with constantly increasing stress and stepped stress increments until the fracture of prismatic marble specimens, were analyzed in terms of non-extensive statistical mechanics (NESM). Initially introduced by Tsallis, NESM has proven to be an autonomous robust theoretical framework for studying fracture mechanisms and damage evolution processes during fracture experiments in specimens made of brittle materials. In the current work, the time intervals of the recorded AE data are analyzed in terms of NESM. For each examined specimen, the corresponding q entropic indices and the βq parameters were calculated, and their variability in terms of the stress applied were studied. Furthermore, a possible linear relationship between the entropic index q and the parameter βq was examined, and it was investigated whether the observed deviation from monotonicity between q and βq may signal increased accumulation of damage, eventually leading to the final fracture of the specimens. Through this work, the emergence of an additional pre-failure indicator (i.e., the deviation from monotonicity between q and βq) alongside well-established ones can provide further insight regarding the underlying crack development mechanisms and damage accumulation processes during the fracture of rock materials.
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37

Chung, Won Sang. « Deformation of the Classical Mechanics by Using the q-Derivative Emerging in the Non-extensive Statistical Mechanics ». International Journal of Theoretical Physics 52, no 10 (13 juin 2013) : 3762–70. http://dx.doi.org/10.1007/s10773-013-1681-5.

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38

INOUE, JUN-ICHI, et KATSUMI TABUSHI. « A GENERALIZATION OF THE DETERMINISTIC ANNEALING EM ALGORITHM BY MEANS OF NON-EXTENSIVE STATISTICAL MECHANICS ». International Journal of Modern Physics B 17, no 29 (20 novembre 2003) : 5525–39. http://dx.doi.org/10.1142/s0217979203023197.

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We extend the EM algorithm to overcome its bottleneck, that is to say, the problem of local maxima of the marginal likelihood due to its strong dependence of initial conditions. As an alternative posterior distribution appearing in the so-called Q function, we use the distribution that maximizes the non-extensive Tsallis entropy. The distribution we introduce has a parameter q which represents the non-extensive property of the entropy. We control the parameter q so as to weaken the influence of the initial conditions. In order to investigate its performance, we apply our algorithm to Gaussian mixture estimation problems under some additive noises. In large data limit, we derive the averaged update equations with respect to hyper-parameters, marginal likelihood etc. analytically. Our analysis supports usefulness of our algorithm.
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39

Zhao, Pan, et Qingxian Xiao. « Variance-Optimal Hedging for the Process Based on Non-Extensive Statistical Mechanics and Poisson Jumps ». Acta Physica Polonica A 129, no 6 (juin 2016) : 1252–56. http://dx.doi.org/10.12693/aphyspola.129.1252.

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40

Zhao, Pan, Benda Zhou et Jixia Wang. « Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics ». Entropy 20, no 1 (18 janvier 2018) : 71. http://dx.doi.org/10.3390/e20010071.

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41

Burud, Nitin B., et J. M. Chandra Kishen. « Non-extensive statistical mechanics for acoustic emission in disordered media : Entropy, size effect, and self-organization ». International Journal of Mechanical Sciences 202-203 (juillet 2021) : 106514. http://dx.doi.org/10.1016/j.ijmecsci.2021.106514.

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42

Wang, Jixia, Pan Zhao et Qinghui Gao. « Portfolio selection problem with nonlinear wealth equations under non-extensive statistical mechanics for time-varying SDE ». Computers & ; Mathematics with Applications 77, no 2 (janvier 2019) : 555–64. http://dx.doi.org/10.1016/j.camwa.2018.09.057.

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43

Sigalotti, Leonardo Di G., Alejandro Ramírez-Rojas et Carlos A. Vargas. « Tsallis q-Statistics in Seismology ». Entropy 25, no 3 (23 février 2023) : 408. http://dx.doi.org/10.3390/e25030408.

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Non-extensive statistical mechanics (or q-statistics) is based on the so-called non-additive Tsallis entropy. Since its introduction by Tsallis, in 1988, as a generalization of the Boltzmann–Gibbs equilibrium statistical mechanics, it has steadily gained ground as a suitable theory for the description of the statistical properties of non-equilibrium complex systems. Therefore, it has been applied to numerous phenomena, including real seismicity. In particular, Tsallis entropy is expected to provide a guiding principle to reveal novel aspects of complex dynamical systems with catastrophes, such as seismic events. The exploration of the existing connections between Tsallis formalism and real seismicity has been the focus of extensive research activity in the last two decades. In particular, Tsallis q-statistics has provided a unified framework for the description of the collective properties of earthquakes and faults. Despite this progress, our present knowledge of the physical processes leading to the initiation of a rupture, and its subsequent growth through a fault system, remains quite limited. The aim of this paper was to provide an overview of the non-extensive interpretation of seismicity, along with the contributions of the Tsallis formalism to the statistical description of seismic events.
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44

Ogunsua, B. O., et J. A. Laoye. « Tsallis non-extensive statistical mechanics in the ionospheric detrended total electron content during quiet and storm periods ». Physica A : Statistical Mechanics and its Applications 497 (mai 2018) : 236–45. http://dx.doi.org/10.1016/j.physa.2018.01.013.

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45

Pessah, M. E., Diego F. Torres et H. Vucetich. « Statistical mechanics and the description of the early universe. (I). Foundations for a slightly non-extensive cosmology ». Physica A : Statistical Mechanics and its Applications 297, no 1-2 (août 2001) : 164–200. http://dx.doi.org/10.1016/s0378-4371(01)00235-7.

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46

Mejrhit, K., et S.-E. Ennadifi. « Thermodynamics, stability and Hawking–Page transition of black holes from non-extensive statistical mechanics in quantum geometry ». Physics Letters B 794 (juillet 2019) : 45–49. http://dx.doi.org/10.1016/j.physletb.2019.03.055.

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47

Sharifian, M., H. R. Sharifinejad, M. Borhani Zarandi et A. R. Niknam. « Effect of q-non-extensive distribution of electrons on the plasma sheath floating potential ». Journal of Plasma Physics 80, no 4 (9 avril 2014) : 607–18. http://dx.doi.org/10.1017/s0022377813000688.

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In this paper, a collisionless unmagnetized plasma sheath consisting of electrons following non-extensive q-distribution, and cold mobile inertial ions is studied in the stationary state. In this type of plasma with non-Maxwellian electron distribution (Tsallis statistical mechanics), the effective electron temperature (Te, eff) and electron screening temperature (Te,*) are evaluated. The other plasma sheath phenomena such as the Bohm sheath criterion, Debye shielding, floating potential, and sheath length are investigated in the presence of q-non-extensive velocity-distributed electrons. It is observed that above-mentioned phenomena depend significantly on the non-extensive parameter q.
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48

BAĞCI, G. B., ALTUĞ ARDA et RAMAZAN SEVER. « QUANTUM MECHANICAL TREATMENT OF THE PROBLEM OF CONSTRAINTS IN NON-EXTENSIVE FORMALISM REVISITED ». Modern Physics Letters B 21, no 16 (10 juillet 2007) : 981–85. http://dx.doi.org/10.1142/s0217984907013390.

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The purity of Werner state in non-extensive formalism associated with two different constraints has been calculated in a previous paper by Bağci et al.17 Two different results have been obtained corresponding to ordinary probability and escort probability. The former has been shown to result in negative values thereby leading authors to deduce the advantage of escort probabilities over ordinary probabilities. However, these results have only been for a limited interval of q values which lie between 0 and 1. In this paper, we solve the same problem for all values of non-extensive index q by using a perturbative approach and show that the simultaneous use of both types of constraint is necessary in order to obtain the solution for a whole spectrum of non-extensive index. In this sense, the existence of these different constraints in non-extensive formalism must not be seen as a deficiency in the formalism but rather must be welcomed as a means of providing solution for all values of parameter q.
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49

TEWELDEBERHAN, A. M., H. G. MILLER et R. TEGEN. « κ-DEFORMED STATISTICS AND THE FORMATION OF A QUARK-GLUON PLASMA ». International Journal of Modern Physics E 12, no 05 (octobre 2003) : 669–73. http://dx.doi.org/10.1142/s021830130300148x.

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The effect of the non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP) has been recently investigated in Ref. 1. The results show that for small deviations (≈ 10%) from Boltzmann–Gibbs (BG) statistics in the QGP phase, the critical temperature for the formation of a QGP does not change substantially for a large variation of the chemical potential. In the present paper we use the extensive κ-deformed statistical mechanics constructed by Kaniadakis to represent the constituents of the QGP and compare the results with Ref. 1.
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50

Wang, Jixia, et Yameng Zhang. « Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model ». Entropy 20, no 11 (28 octobre 2018) : 828. http://dx.doi.org/10.3390/e20110828.

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This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.
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