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Journal articles on the topic 'NON-EXTENSIVE ENTROPY'

Author: Grafiati

Published: 11 September 2023

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1

Tatsuaki, Wada, and Saito Takeshi. "When non-extensive entropy becomes extensive." Physica A: Statistical Mechanics and its Applications 301, no. 1-4 (2001): 284–90. http://dx.doi.org/10.1016/s0378-4371(01)00400-9.

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2

Parvan, A. S., and T. S. Biró. "Extensive Rényi statistics from non-extensive entropy." Physics Letters A 340, no. 5-6 (2005): 375–87. http://dx.doi.org/10.1016/j.physleta.2005.04.036.

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3

Kang, Jin-Wen, Ke-Ming Shen, and Ben-Wei Zhang. "A Note on the Connection between Non-Additive Entropy and h-Derivative." Entropy 25, no. 6 (2023): 918. http://dx.doi.org/10.3390/e25060918.

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In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the h-derivative, which generalizes the conventional Newton–Leibniz calculus. This new entropy, Sh,h′, is proved to describe the non-extensive systems and recover several types of well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann–Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.

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4

Lieb, Elliott H., and Jakob Yngvason. "Entropy meters and the entropy of non-extensive systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2167 (2014): 20140192. http://dx.doi.org/10.1098/rspa.2014.0192.

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In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states, we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This leaves open the question of defining the entropy of macroscopic, but unscalable systems, such as gravitating bodies or systems where surface effects are important. We show here how the problem can be overcome, in principle, with the aid of an ‘entropy meter’. An entropy meter can also be used to determine entropy functions for non-equilibrium states and mesoscopic systems.

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5

Sattin, F. "Non-Extensive Entropy from Incomplete Knowledge of Shannon Entropy?" Physica Scripta 71, no. 5 (2005): 443–46. http://dx.doi.org/10.1238/physica.regular.071a00443.

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6

Bergamelli, Michele, Jan Novotný, and Giovanni Urga. "Maximum Non-Extensive Entropy Block Bootstrap for Non-stationary Processes." Articles 91, no. 1-2 (2016): 115–39. http://dx.doi.org/10.7202/1036916ar.

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In this paper, we propose a novel entropy-based resampling scheme valid for non-stationary data. In particular, we identify the reason for the failure of the original entropy-based algorithm of Vinod and López-de Lacalle (2009) to be the perfect rank correlation between the actual and bootstrapped time series. We propose the Maximum Entropy Block Bootstrap which preserves the rank correlation locally. Further, we also introduce the Maximum non-extensive Entropy Block Bootstrap to allow for fat tail behaviour in time series. Finally, we show the optimal finite sample properties of the proposed methods via a Monte Carlo analysis where we bootstrap the distribution of the Dickey-Fuller test.

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7

Leubner, M. P. "Consequences of entropy bifurcation in non-Maxwellian astrophysical environments." Nonlinear Processes in Geophysics 15, no. 4 (2008): 531–40. http://dx.doi.org/10.5194/npg-15-531-2008.

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Abstract. Non-extensive systems, accounting for long-range interactions and correlations, are fundamentally related to non-Maxwellian distributions where a duality of equilibria appears in two families, the non-extensive thermodynamic equilibria and the kinetic equilibria. Both states emerge out of particular entropy generalization leading to a class of probability distributions, where bifurcation into two stationary states is naturally introduced by finite positive or negative values of the involved entropic index kappa. The limiting Boltzmann-Gibbs-Shannon state (BGS), neglecting any kind of interactions within the system, is subject to infinite entropic index and thus characterized by self-duality. Fundamental consequences of non-extensive entropy bifurcation, manifest in different astrophysical environments, as particular core-halo patterns of solar wind velocity distributions, the probability distributions of the differences of the fluctuations in plasma turbulence as well as the structure of density distributions in stellar gravitational equilibrium are discussed. In all cases a lower entropy core is accompanied by a higher entropy halo state as compared to the standard BGS solution. Data analysis and comparison with high resolution observations significantly support the theoretical requirement of non-extensive entropy generalization when dealing with systems subject to long-range interactions and correlations.

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8

Algin, Abdullah. "Non-extensive entropy of bosonic Fibonacci oscillators." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 04 (2009): P04007. http://dx.doi.org/10.1088/1742-5468/2009/04/p04007.

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9

Oikonomou, Th. "Properties of the “non-extensive Gaussian” entropy." Physica A: Statistical Mechanics and its Applications 381 (July 2007): 155–63. http://dx.doi.org/10.1016/j.physa.2007.03.010.

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10

Jizba, Petr, and Jan Korbel. "On q-non-extensive statistics with non-Tsallisian entropy." Physica A: Statistical Mechanics and its Applications 444 (February 2016): 808–27. http://dx.doi.org/10.1016/j.physa.2015.10.084.

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11

Khordad, R., A. Ghanbari, and A. Ghaffaripour. "Effect of confining potential on information entropy measures in hydrogen atom: extensive and non-extensive entropy." Indian Journal of Physics 94, no. 12 (2019): 2073–79. http://dx.doi.org/10.1007/s12648-019-01654-w.

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12

Rebollo-Neira, L., A. Plastino, and J. Fernandez-Rubio. "On the q= non-extensive maximum entropy distribution." Physica A: Statistical Mechanics and its Applications 258, no. 3-4 (1998): 458–65. http://dx.doi.org/10.1016/s0378-4371(98)00116-2.

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13

Lavagno, A., and P. Narayana Swamy. "Non-extensive entropy in q-deformed quantum groups." Chaos, Solitons & Fractals 13, no. 3 (2002): 437–44. http://dx.doi.org/10.1016/s0960-0779(01)00025-x.

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14

Quarati, P., and A. M. Scarfone. "Non-extensive thermostatistics approach to metal melting entropy." Physica A: Statistical Mechanics and its Applications 392, no. 24 (2013): 6512–22. http://dx.doi.org/10.1016/j.physa.2013.08.020.

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15

Ilić, Velimir M., and Miomir S. Stanković. "Comments on “On q-non-extensive statistics with non-Tsallisian entropy”." Physica A: Statistical Mechanics and its Applications 466 (January 2017): 160–65. http://dx.doi.org/10.1016/j.physa.2016.08.078.

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16

Chung, Won Sang. "Two parameter deformed non-extensive entropy from the two." International Journal of Thermodynamics 19, no. 3 (2016): 158. http://dx.doi.org/10.5541/ijot.5000160131.

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17

Provata, A. "Non-extensive block entropy statistics of Cantor fractal sets." Physica A: Statistical Mechanics and its Applications 381 (July 2007): 148–54. http://dx.doi.org/10.1016/j.physa.2007.03.055.

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18

Trindade, M. A. S., and J. D. M. Vianna. "Non-extensive statistical entropy, quantum groups and quantum entanglement." Physica A: Statistical Mechanics and its Applications 391, no. 12 (2012): 3413–16. http://dx.doi.org/10.1016/j.physa.2012.01.022.

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19

Zaripov, R. G. "Geometry of entropy functions in the extended parastatistics of non-extensive systems." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 5 (2021): 136–40. http://dx.doi.org/10.17223/00213411/64/5/136.

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The group of functions of parametric quantum entropy in extended parastatistics of nonextensive systems is determined. The metric function of Finsler geometry in the two-dimensional space of entropy functions is introduced.

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20

Biró, Tamás, and Zsolt Schram. "Non-Extensive Entropic Distance Based on Diffusion: Restrictions on Parameters in Entropy Formulae." Entropy 18, no. 2 (2016): 42. http://dx.doi.org/10.3390/e18020042.

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21

Wilk, Grzegorz, and Zbigniew Włodarczyk. "Some Non-Obvious Consequences of Non-Extensiveness of Entropy." Entropy 25, no. 3 (2023): 474. http://dx.doi.org/10.3390/e25030474.

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Non-additive (or non-extensive) entropies have long been intensively studied and used in various fields of scientific research. This was due to the desire to describe the commonly observed quasi-power rather than the exponential nature of various distributions of the variables of interest when considered in the full available space of their variability. In this work we will concentrate on the example of high energy multiparticle production processes and will limit ourselves to only one form of non-extensive entropy, namely the Tsallis entropy. We will discuss some points not yet fully clarified and present some non-obvious consequences of non-extensiveness of entropy when applied to production processes.

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22

Vallianatos, F. "A non-extensive approach to risk assessment." Natural Hazards and Earth System Sciences 9, no. 1 (2009): 211–16. http://dx.doi.org/10.5194/nhess-9-211-2009.

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Abstract. We analytically estimate the risk function of natural hazards (earthquakes, rockfalls, forestfires, landslides) by means of a non-extensive approach which is based on implementing the Tsallis entropy for the estimation of the probability density function (PDF) and introducing a phenomenological exponential expression for the damage function. The result leads to a power law expression as a special case and the b-value is given as a function of the non-extensive parameter q. A discussion of risk function dependence on the parameters of hazard PDF and damage function for various hazards is given.

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23

Irshad, Muhammed Rasheed, Radhakumari Maya, Francesco Buono та Maria Longobardi. "Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data". Entropy 24, № 1 (2021): 9. http://dx.doi.org/10.3390/e24010009.

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Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

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24

Buiatti, Marco, Paolo Grigolini, and Luigi Palatella. "A non extensive approach to the entropy of symbolic sequences." Physica A: Statistical Mechanics and its Applications 268, no. 1-2 (1999): 214–24. http://dx.doi.org/10.1016/s0378-4371(99)00062-x.

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25

Robledo, A., and J. Quintana. "Scale-invariant random-walks and optimization of non-extensive entropy." Chaos, Solitons & Fractals 13, no. 3 (2002): 521–28. http://dx.doi.org/10.1016/s0960-0779(01)00035-2.

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26

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

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27

Shafee, F. "Lambert function and a new non-extensive form of entropy." IMA Journal of Applied Mathematics 72, no. 6 (2007): 785–800. http://dx.doi.org/10.1093/imamat/hxm039.

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28

Deppman, Airton, Tobias Frederico, Eugenio Megías, and Debora Menezes. "Fractal Structure and Non-Extensive Statistics." Entropy 20, no. 9 (2018): 633. http://dx.doi.org/10.3390/e20090633.

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The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics have been discussed in detail in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non-extensive statistics have been formulated over the last several years, in particular a fractal structure in thermodynamic functions was recently proposed as a possible origin for non-extensive statistics in physical systems. In the present work, we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such a system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that provided evidence of the connections between those fluctuations and Tsallis statistics. Finally, the scale invariance of the fractal thermodynamical system is discussed in terms of the Callan–Symanzik equation.

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29

Zaripov, R. G. "On thermal equilibrium in extended parastatistics of non-extensive systems." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 3 (2021): 126–31. http://dx.doi.org/10.17223/00213411/64/3/126.

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Trigonometric entropies are introduced in the extended parastatistics of nonextensive systems and their properties are given. The equilibrium states of systems with corresponding distributions are considered for the general dependence of entropies on the angle in the two-dimensional space of entropy functions.

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30

Yoon, Peter H. "Thermodynamic, Non-Extensive, or Turbulent Quasi-Equilibrium for the Space Plasma Environment." Entropy 21, no. 9 (2019): 820. http://dx.doi.org/10.3390/e21090820.

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The Boltzmann–Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is additive and extensive, but for certain systems such as those dictated by long-range interactions, it is speculated that the entropy must be non-additive and non-extensive. Tsallis entropy possesses these characteristics, and is parameterized by a variable q ( q = 1 being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains a phenomenological tool. To this day, very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from microphysics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in a quasi-equilibrium state with electrostatic turbulence known as quasi-thermal noise, it is shown that the value corresponding to q = 9 / 13 = 0 . 6923 , or alternatively q = 5 / 9 = 0 . 5556 , may be deduced. This prediction is verified against observations made by spacecraft, and it is shown to be in excellent agreement. This paper constitutes an overview of recent developments regarding the non-equilibrium statistical mechanical approach to understanding the non-extensive nature of space plasma, although some recent new developments are also discussed.

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31

Dragan, G. S., V. V. Kutarov, and A. Y. Bekshaev. "Non-extensive thermodynamics of the radiation in heterogeneous thermal plasmas." Condensed Matter Physics 25, no. 1 (2022): 13502. http://dx.doi.org/10.5488/cmp.25.13502.

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Thermodynamic characteristics of the radiation of condensed combustion products presented in the form of agglomerates of metal-oxide nanoparticles demonstrate deviations from the classical Planck’s law. We propose to interpret these deviations in terms of the non-additive entropy of the photon system interacting with the heterogeneous combustion products, which makes it possible to use the non-extensive Tsallis thermodynamics for their description. It is assumed that the non-additive character of the radiation entropy in heterogeneous plasma can be explained by the influence of long-range interactions and non-equilibrium physicochemical processes. An expression is obtained for the energy-dependent distribution of the photon density, based on the phenomenological parameter of non-extensiveness q which, in the first approximation, does not depend on the energy. In this case, the "non-extensive" Planck’s law can be reduced to the "usual" Planck distribution by introducing the "effective temperature" that exceeds the real temperature. Numerical modelling has shown that the spectral density of photons, the position and magnitude of its maximum depend on the value of the parameter q, which can be used for its experimental determination and revelation of its physical nature and origin.

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32

Bwanakare, Second. "Non-extensive entropy econometrics and CES production models: Country case study." Statistical Journal of the IAOS 32, no. 4 (2016): 709–13. http://dx.doi.org/10.3233/sji-161021.

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33

Susan, Seba, and Madasu Hanmandlu. "A non-extensive entropy feature and its application to texture classification." Neurocomputing 120 (November 2013): 214–25. http://dx.doi.org/10.1016/j.neucom.2012.08.059.

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34

Ramírez-Pacheco, Julio, Joel Trejo-Sánchez, Joaquin Cortez-González, and Ramón Palacio. "Classification of Fractal Signals Using Two-Parameter Non-Extensive Wavelet Entropy." Entropy 19, no. 5 (2017): 224. http://dx.doi.org/10.3390/e19050224.

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35

Susan, Seba, Rahul Singh, Amit Kumar, Abhishek Kumar, and Ashwani Kumar. "Segmentation of Dark Foreground Objects by Maximum Non-Extensive Entropy Partitioning." International Journal of Applied Research on Information Technology and Computing 9, no. 1 (2018): 67. http://dx.doi.org/10.5958/0975-8089.2018.00007.6.

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36

Rodrigues, Paulo S., and Gilson A. Giraldi. "Improving the non-extensive medical image segmentation based on Tsallis entropy." Pattern Analysis and Applications 14, no. 4 (2011): 369–79. http://dx.doi.org/10.1007/s10044-011-0225-y.

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37

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

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38

Bahramiyan, H., R. Khordad, and H. R. Rastegar Sedehi. "Non-extensive entropy of modified Gaussian quantum dot under polaron effects." Indian Journal of Physics 92, no. 7 (2018): 941–45. http://dx.doi.org/10.1007/s12648-018-1168-6.

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39

Khordad, R., and H. R. Rastegar Sedehi. "Study of non-extensive entropy of bound polaron in monolayer graphene." Indian Journal of Physics 92, no. 8 (2018): 979–84. http://dx.doi.org/10.1007/s12648-018-1192-6.

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40

Khordad, R., and H. R. Rastegar Sedehi. "Application of non-extensive entropy to study of decoherence of RbCl quantum dot qubit: Tsallis entropy." Superlattices and Microstructures 101 (January 2017): 559–66. http://dx.doi.org/10.1016/j.spmi.2016.10.041.

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41

Kolesnichenko, Aleksandr Vladimirovich, and Mikhail Yakovlevich Marov. "Scenario of accelerated universe expansion under exposure to entropic forces related to with the entropies of Barrow and Tsallis−Cirto." Mathematica Montisnigri 50 (2021): 80–103. http://dx.doi.org/10.20948/mathmontis-2021-50-8.

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In the work within the framework of "entropic cosmology", the scenario of the cosmological accelerated expansion of a flat, homogeneous and isotropic Universe under the influence of entropic forces is considered without the concept of dark energy a hypothetical medium with negative pressure. Assuming that the horizon of the Universe has its own temperature and entropy, which arises during the holographic storage of information on the screen of the horizon surface, the entropy models of the Universe associated with the BekensteinHawking entropy and the non-extensive Barrow and Tsallis–Cirto entropies are considered. The modified equations of acceleration and continuity of Friedman with governing power terms having an entropic nature are derived both within the framework of Einstein's general theory of relativity and on the basis of a thermodynamic approach that allows modeling the non-adiabatic evolution of the Universe. At the same time, models based on nonextensive entropies predict the existence of both a decelerating and accelerating Universe.

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42

Ghanbari, Ahmad, Reza Khordad, and Mostafa Ghaderi-Zefrehei. "Non-extensive thermodynamic entropy to predict the dynamics behavior of COVID-19." Physica B: Condensed Matter 624 (January 2022): 413448. http://dx.doi.org/10.1016/j.physb.2021.413448.

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43

Tapiero, Oren J. "A maximum (non-extensive) entropy approach to equity options bid–ask spread." Physica A: Statistical Mechanics and its Applications 392, no. 14 (2013): 3051–60. http://dx.doi.org/10.1016/j.physa.2013.03.015.

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44

Susan, Seba, and Madasu Hanmandlu. "Color texture recognition by color information fusion using the non-extensive entropy." Multidimensional Systems and Signal Processing 29, no. 4 (2017): 1269–84. http://dx.doi.org/10.1007/s11045-017-0502-z.

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45

OU, CONGJIE, AZIZ EL KAABOUCHI, JINCAN CHEN, ALAIN LE MÉHAUTÉ, and ALEXANDRE QIUPING WANG. "GENERALIZED MEASURE OF UNCERTAINTY AND THE MAXIMIZABLE ENTROPY." Modern Physics Letters B 24, no. 09 (2010): 825–31. http://dx.doi.org/10.1142/s0217984910022883.

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For a random variable x we can define a variational relationship with practical physical meaning as [Formula: see text], where I is the uncertainty measure. With the help of a generalized definition of expectation, [Formula: see text], we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g({pi}) may have different forms for different statistical methods which include the extensive and non-extensive statistics. Moreover, it is pointed out that this generalized uncertainty measure is valid not only for thermodynamic systems but also for non-thermodynamic systems.

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46

INOUE, JUN-ICHI, and 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 (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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47

Kalogeropoulos, Nikos. "Almost additive entropy." International Journal of Geometric Methods in Modern Physics 11, no. 05 (2014): 1450040. http://dx.doi.org/10.1142/s0219887814500406.

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We explore consequences of a hyperbolic metric induced by the composition property of the Harvda–Charvat/Daróczy/Cressie–Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter q ≈ 1 from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.

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48

Robledo, A. "The renormalization group and optimization of non-extensive entropy: criticality in non-linear one-dimensional maps." Physica A: Statistical Mechanics and its Applications 314, no. 1-4 (2002): 437–41. http://dx.doi.org/10.1016/s0378-4371(02)01177-9.

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49

Rebollo-Neira, L., J. Fernandez-Rubio, and A. Plastino. "A non-extensive maximum entropy based regularization method for bad conditioned inverse problems." Physica A: Statistical Mechanics and its Applications 261, no. 3-4 (1998): 555–68. http://dx.doi.org/10.1016/s0378-4371(98)00400-2.

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50

Topsøe, Flemming. "Factorization and escorting in the game-theoretical approach to non-extensive entropy measures." Physica A: Statistical Mechanics and its Applications 365, no. 1 (2006): 91–95. http://dx.doi.org/10.1016/j.physa.2006.01.024.

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