IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v387y2008i11p2462-2470.html
   My bibliography  Save this article

Pathway parameter and thermonuclear functions

Author

Listed:
  • Mathai, A.M.
  • Haubold, H.J.

Abstract

In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell–Boltzmann distribution function were considered in a series of papers by Mathai and Haubold [A.M. Mathai, H.J. Haubold, Modern Problems in Nuclear and Neutrino Astrophysics, Akademie-Verlag, Berlin, 1988]. In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter α, so that when α→1 the thermonuclear functions in the Maxwell–Boltzmannian case are recovered. We will also give interpretations for the pathway parameter α in the case of cut-off and in terms of moments. Non-extensive statistical mechanics, as developed by Tsallis [C. Tsallis, What should a statistical mechanics satisfy to reflect nature? Physica D 193 (2004) 3–34], provides the physical basis for the generalized thermonuclear functions considered in this paper.

Suggested Citation

  • Mathai, A.M. & Haubold, H.J., 2008. "Pathway parameter and thermonuclear functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2462-2470.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2462-2470
    DOI: 10.1016/j.physa.2008.01.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108000472
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2008.01.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Saxena, R.K. & Mathai, A.M. & Haubold, H.J., 2004. "Astrophysical thermonuclear functions for Boltzmann–Gibbs statistics and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 649-656.
    2. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lubashevsky, Ihor & Friedrich, Rudolf & Heuer, Andreas & Ushakov, Andrey, 2009. "Generalized superstatistics of nonequilibrium Markovian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4535-4550.
    2. Zhang, Yongping & Shang, Pengjian & Xiong, Hui, 2019. "Multivariate generalized information entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1212-1223.
    3. Han, Jung Hun, 2013. "Gamma function to Beck–Cohen superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4288-4298.
    4. Xu, Meng & Shang, Pengjian & Zhang, Sheng, 2021. "Multiscale Rényi cumulative residual distribution entropy: Reliability analysis of financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Sánchez C., Ewin & Vega-Jorquera, Pedro, 2019. "Modelling temporal decay of aftershocks by a solution of the fractional reactive equation," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 43-49.
    6. Arak M. Mathai & Hans J. Haubold, 2020. "Mathematical Aspects of Krätzel Integral and Krätzel Transform," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    7. Dhannya Joseph, 2011. "Gamma distribution and extensions by using pathway idea," Statistical Papers, Springer, vol. 52(2), pages 309-325, May.
    8. Sánchez C., Ewin & Vega-Jorquera, Pedro, 2018. "New Bayesian frequency–magnitude distribution model for earthquakes applied in Chile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 305-312.
    9. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
    10. Aditya Mani Mishra & Dumitru Baleanu & Fairouz Tchier & Sunil Dutt Purohit, 2019. "Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    11. Jose, K.K. & Naik, Shanoja R., 2008. "A class of asymmetric pathway distributions and an entropy interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(28), pages 6943-6951.
    12. Aswathy S. Krishnan & S. M. Sunoj & P. G. Sankaran, 2019. "Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 17-38, January.
    13. Mohammed Z. Alqarni & Mohamed Abdalla, 2023. "Novel Kinds of Fractional λ –Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral," Mathematics, MDPI, vol. 11(19), pages 1-14, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2462-2470. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.