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Maximum entropy generation and κ-exponential model

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  • Lucia, Umberto

Abstract

An increasing number of natural phenomena appear to deviate from standard statistical distributions. It has kindled interest in alternative formulation of statistical mechanics which should preserve most of the mathematical structures of the Boltzmann–Gibbs theory, while reproducing the phenomenology of the anomalous systems. The κ-theory has obtained a lot of results in the analysis of natural phenomena, but it was not extended to irreversible open systems. A modified κ-theory is proposed for its use in irreversible open systems.

Suggested Citation

  • Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4558-4563
    DOI: 10.1016/j.physa.2010.06.047
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    References listed on IDEAS

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    1. Huang, Zhifu & Ou, Congjie & Méhauté, A. Le & Wang, Qiuping A. & Chen, Jincan, 2009. "Inherent correlations between thermodynamics and statistical physics in extensive and nonextensive systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2331-2336.
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    3. Ou, Congjie & El Kaabouchi, Aziz & Chen, Jincan & Le Méhauté, Alain & Wang, Qiuping A., 2009. "Stability of incomplete entropy and incomplete expectation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1813-1817.
    4. Lucia, Umberto, 2009. "Irreversibility, entropy and incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4025-4033.
    5. Lucia, Umberto, 2008. "Statistical approach of the irreversible entropy variation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3454-3460.
    6. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    7. Martı́nez, S & Nicolás, F & Pennini, F & Plastino, A, 2000. "Tsallis’ entropy maximization procedure revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(3), pages 489-502.
    8. T. Wada & A. M. Scarfone, 2009. "Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 65-71, July.
    9. T. Wada & A. M. Scarfone, 2005. "A non self-referential expression of Tsallis' probability distribution function," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 47(4), pages 557-561, October.
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    Citations

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    Cited by:

    1. Lucia, Umberto, 2013. "Thermodynamic paths and stochastic order in open systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3912-3919.
    2. Açıkkalp, Emin & Caner, Necmettin, 2015. "Determining performance of an irreversible nano scale dual cycle operating with Maxwell–Boltzmann gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 342-349.
    3. Lucia, Umberto, 2016. "Econophysics and bio-chemical engineering thermodynamics: The exergetic analysis of a municipality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 421-430.
    4. Lucia, Umberto, 2014. "Entropy generation and the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 256-260.
    5. Umberto Lucia, 2014. "The Gouy-Stodola Theorem in Bioenergetic Analysis of Living Systems (Irreversibility in Bioenergetics of Living Systems)," Energies, MDPI, vol. 7(9), pages 1-23, September.
    6. Lucia, Umberto, 2014. "Entropy generation approach to cell systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 1-11.

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