IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v247y1997i1p559-569.html
   My bibliography  Save this article

Fisher's information measure in a Tsallis' nonextensive setting and its application to diffusive process

Author

Listed:
  • Pennini, F.
  • Plastino, A.

Abstract

Fisher's information measures, as adapted to a nonextensive (Tsallis) environment, are discussed. For systems of particles that are in a general state of motion a lower bound to these information measures is derived with the help of a recently established upper bound to the entropy increase. This lower bound to the information measure is the basis for a variational principle devised to determine unknown probability distributions. In the important instance of diffusion process we show that trying to ascertain which is the probability distribution that maximizes Fisher's information sheds some light on the meaning of Tsallis' q-parameter. We discuss applications to cosmological models that seem to suggest that a non-extensive thermostatistics with q = −1 provides an adequate scenario for discussing gravitation.

Suggested Citation

  • Pennini, F. & Plastino, A., 1997. "Fisher's information measure in a Tsallis' nonextensive setting and its application to diffusive process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 247(1), pages 559-569.
    • Handle: RePEc:eee:phsmap:v:247:y:1997:i:1:p:559-569
    DOI: 10.1016/S0378-4371(97)00395-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437197003956
    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(97)00395-6?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. James Verdier & Rebecca Dodge & Lisa Chimento & Joel Menges & Moira Forbes, "undated". "Using Data Strategically in Medicaid Managed Care," Mathematica Policy Research Reports a9627d6381e448088b25fe89d, Mathematica Policy Research.
    2. Hassan, S.A. & Kuperman, M.N. & Wio, H.S. & Zanette, D.H., 1994. "Evolution of reaction-diffusion patterns in infinite and bounded domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(3), pages 380-400.
    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. Portesi, M & Plastino, A, 1996. "Generalized entropy as a measure of quantum uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 412-430.
    2. Litvin, Vladimir A., 2004. "Multiscaling behavior in transition economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 178-183.
    3. Litvin, Vladimir A., 2004. "Multiscaling behavior of transition economies before and after 1998 Russian financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 19-23.
    4. Budaev, V.P., 2004. "Turbulence in magnetized plasmas and financial markets: comparative study of multifractal statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 299-307.
    5. Ren, F. & Zheng, B. & Lin, H. & Wen, L.Y. & Trimper, S., 2005. "Persistence probabilities of the German DAX and Shanghai Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 439-450.
    6. Cizeau, Pierre & Liu, Yanhui & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Volatility distribution in the S&P500 stock index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 441-445.
    7. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    8. Plastino, A.R. & Plastino, A., 1995. "Non-extensive statistical mechanics and generalized Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 347-354.
    9. Pennini, F. & Plastino, A. & Plastino, A.R., 1996. "Tsallis nonextensive thermostatistics, Pauli principle and the structure of the Fermi surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 234(1), pages 471-479.
    10. Andricioaei, Ioan & Straub, John E., 1997. "An efficient Monte Carlo algorithm for overcoming broken ergodicity in the simulation of spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 247(1), pages 553-558.
    11. Gamero, L.G. & Plastino, A. & Torres, M.E., 1997. "Wavelet analysis and nonlinear dynamics in a nonextensive setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 487-509.
    12. Kaniadakis, G. & Quarati, P., 1997. "Polynomial expansion of diffusion and drift coefficients for classical and quantum statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 229-239.
    13. Vandewalle, N. & Ausloos, M., 1997. "Coherent and random sequences in financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 454-459.
    14. Pennini, F. & Plastino, A.R. & Plastino, A., 1997. "Dynamical evolution and Tsallis generalized quantum thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 388-406.

    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:247:y:1997:i:1:p:559-569. 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.