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Kaniadakis statistics (also known as κ-statistics) is a generalization of Boltzmann–Gibbs statistical mechanics,[1] based on a relativistic[2][3][4] generalization of the classical Boltzmann–Gibbs–Shannon entropy (commonly referred to as Kaniadakis entropy or κ-entropy). Introduced by the Greek Italian physicist Giorgio Kaniadakis in 2001,[5] κ-statistical mechanics preserve the main features of ordinary statistical mechanics and have attracted the interest of many researchers in recent years. The κ-distribution is currently considered one of the most viable candidates for explaining complex physical,[6][7] natural or artificial systems involving power-law tailed statistical distributions. Kaniadakis statistics have been adopted successfully in the description of a variety of systems in the fields of cosmology, astrophysics,[8][9] condensed matter, quantum physics,[10][11] seismology,[12][13] genomics,[14][15] economics,[16][17] epidemiology,[18] and many others.
^Kaniadakis, G. (2009). "Relativistic entropy and related Boltzmann kinetics". The European Physical Journal A. 40 (3): 275–287. arXiv:0901.1058. Bibcode:2009EPJA...40..275K. doi:10.1140/epja/i2009-10793-6. ISSN 1434-6001. S2CID 119190011.
^Kaniadakis, G. (2002). "Statistical mechanics in the context of special relativity". Physical Review E. 66 (5): 056125. arXiv:cond-mat/0210467. Bibcode:2002PhRvE..66e6125K. doi:10.1103/PhysRevE.66.056125. ISSN 1063-651X. PMID 12513574. S2CID 45635888.
^Kaniadakis, G. (2005). "Statistical mechanics in the context of special relativity. II". Physical Review E. 72 (3): 036108. arXiv:cond-mat/0507311. Bibcode:2005PhRvE..72c6108K. doi:10.1103/PhysRevE.72.036108. ISSN 1539-3755. PMID 16241516. S2CID 18115408.
^Kaniadakis, G. (2011). "Power-law tailed statistical distributions and Lorentz transformations". Physics Letters A. 375 (3): 356–359. arXiv:1110.3944. Bibcode:2011PhLA..375..356K. doi:10.1016/j.physleta.2010.11.057. ISSN 0375-9601. S2CID 118435479.
^Kaniadakis, G. (2001). "Non-linear kinetics underlying generalized statistics". Physica A: Statistical Mechanics and Its Applications. 296 (3): 405–425. arXiv:cond-mat/0103467. Bibcode:2001PhyA..296..405K. doi:10.1016/S0378-4371(01)00184-4. ISSN 0378-4371. S2CID 44275064.
^Kaniadakis, G. (2009). "Maximum entropy principle and power-law tailed distributions". The European Physical Journal B. 70 (1): 3–13. arXiv:0904.4180. Bibcode:2009EPJB...70....3K. doi:10.1140/epjb/e2009-00161-0. ISSN 1434-6028. S2CID 55421804.
^Kaniadakis, G. (2021). "New power-law tailed distributions emerging in κ-statistics (a)". Europhysics Letters. 133 (1): 10002. arXiv:2203.01743. Bibcode:2021EL....13310002K. doi:10.1209/0295-5075/133/10002. ISSN 0295-5075. S2CID 234144356.
^Carvalho, J. C.; Silva, R.; do Nascimento Jr., J. D.; De Medeiros, J. R. (2008). "Power law statistics and stellar rotational velocities in the Pleiades". EPL (Europhysics Letters). 84 (5): 59001. arXiv:0903.0836. Bibcode:2008EL.....8459001C. doi:10.1209/0295-5075/84/59001. ISSN 0295-5075. S2CID 7123391.
^Curé, Michel; Rial, Diego F.; Christen, Alejandra; Cassetti, Julia (2014). "A method to deconvolve stellar rotational velocities". Astronomy & Astrophysics. 565: A85. arXiv:1401.1054. Bibcode:2014A&A...565A..85C. doi:10.1051/0004-6361/201323344. ISSN 0004-6361. S2CID 59375612.
^Abreu, Everton M. C.; Ananias Neto, Jorge; Mendes, Albert C. R.; de Paula, Rodrigo M. (2019). "Loop quantum gravity Immirzi parameter and the Kaniadakis statistics". Chaos, Solitons & Fractals. 118: 307–310. arXiv:1808.01891. Bibcode:2019CSF...118..307A. doi:10.1016/j.chaos.2018.11.033. ISSN 0960-0779. S2CID 119207713.
^Hristopulos, Dionissios T.; Petrakis, Manolis P.; Kaniadakis, Giorgio (2014). "Finite-size effects on return interval distributions for weakest-link-scaling systems". Physical Review E. 89 (5): 052142. arXiv:1308.1881. Bibcode:2014PhRvE..89e2142H. doi:10.1103/PhysRevE.89.052142. ISSN 1539-3755. PMID 25353774. S2CID 22310350.
^da Silva, Sérgio Luiz E. F. (2021). "κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes". Chaos, Solitons & Fractals. 143: 110622. Bibcode:2021CSF...14310622D. doi:10.1016/j.chaos.2020.110622. ISSN 0960-0779. S2CID 234063959.
^Souza, N. T. C. M.; Anselmo, D. H. A. L.; Silva, R.; Vasconcelos, M. S.; Mello, V. D. (2014). "A κ -statistical analysis of the Y-chromosome". EPL (Europhysics Letters). 108 (3): 38004. doi:10.1209/0295-5075/108/38004. ISSN 0295-5075. S2CID 122456729.
^Costa, M. O.; Silva, R.; Anselmo, D. H. A. L.; Silva, J. R. P. (2019). "Analysis of human DNA through power-law statistics". Physical Review E. 99 (2): 022112. Bibcode:2019PhRvE..99b2112C. doi:10.1103/PhysRevE.99.022112. ISSN 2470-0045. PMID 30934358. S2CID 91186653.
^Clementi, Fabio; Gallegati, Mauro; Kaniadakis, Giorgio (2012). "A new model of income distribution: the κ-generalized distribution". Journal of Economics. 105 (1): 63–91. doi:10.1007/s00712-011-0221-0. hdl:11393/73598. ISSN 0931-8658. S2CID 155080665.
^Trivellato, Barbara (2013). "Deformed Exponentials and Applications to Finance". Entropy. 15 (12): 3471–3489. Bibcode:2013Entrp..15.3471T. doi:10.3390/e15093471. ISSN 1099-4300.
^Kaniadakis, Giorgio; Baldi, Mauro M.; Deisboeck, Thomas S.; Grisolia, Giulia; Hristopulos, Dionissios T.; Scarfone, Antonio M.; Sparavigna, Amelia; Wada, Tatsuaki; Lucia, Umberto (2020). "The κ-statistics approach to epidemiology". Scientific Reports. 10 (1): 19949. arXiv:2012.00629. Bibcode:2020NatSR..1019949K. doi:10.1038/s41598-020-76673-3. ISSN 2045-2322. PMC 7673996. PMID 33203913.
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