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Non-linear kinetics underlying generalized statistics

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  • Kaniadakis, G.
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    Abstract

    The purpose of the present effort is threefold. Firstly, it is shown that there exists a principle, that we call kinetical interaction principle (KIP), underlying the non-linear kinetics in particle systems, independently on the picture (Kramers, Boltzmann) used to describe their time evolution. Secondly, the KIP imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution, both as stationary solution of the non-linear evolution equation and as the state which maximizes the generalized entropy. Thirdly, the KIP allows, on one hand, to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and, on the other hand, suggests how we can introduce naturally new distributions. Finally, as a working example of the approach to the non-linear kinetics here presented, a new non-extensive statistics is constructed and studied starting from a one-parameter deformation of the exponential function holding the relation f(−x)f(x)=1.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437101001844
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 296 (2001)
    Issue (Month): 3 ()
    Pages: 405-425

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    Handle: RePEc:eee:phsmap:v:296:y:2001:i:3:p:405-425

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Non-linear kinetics; Generalized entropy; H-theorem;

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    Cited by:
    1. Fabio Clementi & Mauro Gallegati, 2005. "Pareto's Law of Income Distribution: Evidence for Grermany, the United Kingdom, and the United States," Microeconomics 0505006, EconWPA.
    2. Amblard, Pierre-Olivier & Vignat, Christophe, 2006. "A note on bounded entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 50-56.
    3. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    4. Maria Letizia Bertotti & Giovanni Modanese, 2014. "Micro to macro models for income distribution in the absence and in the presence of tax evasion," Papers 1403.0015, arXiv.org.
    5. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2012. "A new model of income distribution: the κ-generalized distribution," Journal of Economics, Springer, vol. 105(1), pages 63-91, January.
    6. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    7. Rajaonarison, Dominique, 2008. "Deterministic heterogeneity in tastes and product differentiation in the K-logit model," Economics Letters, Elsevier, vol. 100(3), pages 396-398, September.
    8. Ván, P., 2006. "Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 28-33.
    9. Rajaonarison, Dominique & Bolduc, Denis & Jayet, Hubert, 2005. "The K-deformed multinomial logit model," Economics Letters, Elsevier, vol. 86(1), pages 13-20, January.
    10. Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
    11. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.

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