IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i16p3117-3127.html
   My bibliography  Save this article

The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models

Author

Listed:
  • Ali, S.A.
  • Cafaro, C.
  • Kim, D.-H.
  • Mancini, S.

Abstract

We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between microvariables). We observe a power law decay of the IGC at a rate determined by the correlation coefficient. It is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in the absence of microcorrelations. This finding uncovers an important connection between (micro)correlations and (macro)complexity in Gaussian statistical dynamical systems.

Suggested Citation

  • Ali, S.A. & Cafaro, C. & Kim, D.-H. & Mancini, S., 2010. "The effect of microscopic correlations on the information geometric complexity of Gaussian statistical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3117-3127.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3117-3127
    DOI: 10.1016/j.physa.2010.03.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110002724
    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.2010.03.028?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. Cafaro, Carlo, 2009. "Works on an information geometrodynamical approach to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 886-891.
    2. Lebowitz, Joel L., 1999. "Microscopic origins of irreversible macroscopic behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 516-527.
    3. Lebowitz, Joel L., 1993. "Macroscopic laws, microscopic dynamics, time's arrow and Boltzmann's entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 1-27.
    4. Cafaro, C. & Ali, S.A., 2008. "Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6876-6894.
    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. Kazan, Ahmet, 2019. "Conformally-projectively flat trans-Sasakian statistical manifolds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Gomez, Ignacio S. & Portesi, Mariela & Borges, Ernesto P., 2020. "Universality classes for the Fisher metric derived from relative group entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).

    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. Pérez-Cárdenas, Fernando C. & Resca, Lorenzo & Pegg, Ian L., 2016. "Microscopic reversibility and macroscopic irreversibility: A lattice gas model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 82-92.
    2. Michel, Denis, 2018. "A probabilistic rate theory connecting kinetics to thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 26-44.
    3. Lebed, Igor V., 2019. "The cause for emergence of irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 325-341.
    4. Kalogeropoulos, Nikolaos, 2022. "Coarse-graining and symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    5. Giffin, Adom & Cafaro, Carlo & Ali, Sean Alan, 2016. "Application of the maximum relative entropy method to the physics of ferromagnetic materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 11-26.
    6. Kalogeropoulos, Nikolaos, 2018. "Time irreversibility from symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 202-210.
    7. Gorban, Alexander, 2007. "Order–disorder separation: Geometric revision," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 85-102.
    8. Waldner, Franz & Hoover, William G. & Hoover, Carol G., 2014. "The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 68-76.
    9. Cafaro, Carlo & Mancini, Stefano, 2012. "On Grover’s search algorithm from a quantum information geometry viewpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1610-1625.
    10. Creaco, Anthony J. & Kalogeropoulos, Nikolaos, 2019. "Irreversibility from staircases in symplectic embeddings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 497-509.

    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:389:y:2010:i:16:p:3117-3127. 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.