IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v296y2001i3p405-425.html
   My bibliography  Save this article

Non-linear kinetics underlying generalized statistics

Author

Listed:
  • Kaniadakis, G.

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.

Suggested Citation

  • Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    • Handle: RePEc:eee:phsmap:v:296:y:2001:i:3:p:405-425
    DOI: 10.1016/S0378-4371(01)00184-4
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437101001844
    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/S0378-4371(01)00184-4?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.

    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:296:y:2001:i:3:p:405-425. 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.