IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v385y2007i2p493-500.html
   My bibliography  Save this article

On generalized entropy measures and pathways

Author

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

Abstract

Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic functional form for Shannon entropy. Due to the logarithmic nature, Shannon entropy naturally gives rise to additivity, when applied to situations having product probability property. It is argued that the natural process is non-additivity, important, for example, in statistical mechanics [C. Tsallis, Possible generalization of Boltzmann–Gibbs statistics, J. Stat. Phys. 52 (1988) 479–487; E.G.D. Cohen, Boltzmann and Einstein: statistics and dynamics—an unsolved problem, Pramana 64 (2005) 635–643.], even in product probability property situations and additivity can hold due to the involvement of a recursivity postulate leading to a logarithmic function. Generalized entropies are introduced and some of their properties are examined. Situations are examined where a generalized entropy of order α leads to pathway models, exponential and power law behavior and related differential equations. Connection of this entropy to Kerridge's measure of “inaccuracy” is also explored.

Suggested Citation

  • Mathai, A.M. & Haubold, H.J., 2007. "On generalized entropy measures and pathways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 493-500.
  • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:493-500
    DOI: 10.1016/j.physa.2007.06.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107007157
    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.2007.06.047?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. Beck, Christian, 2006. "Stretched exponentials from superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 96-101.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tanita Botha & Johannes Ferreira & Andriette Bekker, 2021. "Alternative Dirichlet Priors for Estimating Entropy via a Power Sum Functional," Mathematics, MDPI, vol. 9(13), pages 1-17, June.

    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. Han, Jung Hun, 2013. "Gamma function to Beck–Cohen superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4288-4298.
    3. Brownlee, R.A. & Gorban, A.N. & Levesley, J., 2008. "Nonequilibrium entropy limiters in lattice Boltzmann methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 385-406.
    4. Yusuke Uchiyama & Takanori Kadoya, 2018. "Superstatistics with cut-off tails for financial time series," Papers 1809.04775, arXiv.org.
    5. K. Jose & Shanoja Naik & Miroslav Ristić, 2010. "Marshall–Olkin q-Weibull distribution and max–min processes," Statistical Papers, Springer, vol. 51(4), pages 837-851, December.
    6. Mathai, A.M. & Provost, Serge B., 2013. "Generalized Boltzmann factors induced by Weibull-type distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 545-551.
    7. Dhannya Joseph, 2011. "Gamma distribution and extensions by using pathway idea," Statistical Papers, Springer, vol. 52(2), pages 309-325, May.
    8. 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.
    9. 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.

    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:385:y:2007:i:2:p:493-500. 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.