IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v334y2004i3p444-458.html
   My bibliography  Save this article

The constrained entropy and cross-entropy functions

Author

Listed:
  • Niven, Robert K.

Abstract

This study introduces the constrained forms of the Shannon information entropy and Kullback–Leibler cross-entropy functions. Applicable to a closed system, these functions incorporate the constraints on the system in a generic fashion, irrespective of the form or even the number of the constraints. Since they are fully constrained, the constrained functions may be “pulled apart” to give their partial or local constrained forms, providing the means to examine the probability of each outcome or state relative to its local maximum entropy (or minimum cross-entropy) position, independently of the other states of the system. The Shannon entropy and Kullback–Leibler cross-entropy functions do not possess this functionality. The features of each function are examined in detail, and the similarities between the constrained and Tsallis entropy functions are examined. The continuous constrained entropy and cross-entropy functions are also introduced, the integrands of which may be used to independently examine each infinitesimal state (physical element) of the system.

Suggested Citation

  • Niven, Robert K., 2004. "The constrained entropy and cross-entropy functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(3), pages 444-458.
    • Handle: RePEc:eee:phsmap:v:334:y:2004:i:3:p:444-458
    DOI: 10.1016/j.physa.2003.11.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437103011087
    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.2003.11.011?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.

    Citations

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


    Cited by:

    1. Singh, Vijay P. & Oh, Juik, 2015. "A Tsallis entropy-based redundancy measure for water distribution networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 360-376.

    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:334:y:2004:i:3:p:444-458. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.