IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v576y2021ics0378437121003344.html
   My bibliography  Save this article

Information geometry for Fermi–Dirac and Bose–Einstein quantum statistics

Author

Listed:
  • Pessoa, Pedro
  • Cafaro, Carlo

Abstract

Information geometry is an emergent branch of probability theory that consists of assigning a Riemannian differential geometry structure to the space of probability distributions. We present an information geometric investigation of gases following the Fermi–Dirac and the Bose–Einstein quantum statistics. For each quantum gas, we study the information geometry of the curved statistical manifolds associated with the grand canonical ensemble. The Fisher–Rao information metric and the scalar curvature are computed for both fermionic and bosonic models of non-interacting particles. In particular, by taking into account the ground state of the ideal bosonic gas in our information geometric analysis, we find that the singular behavior of the scalar curvature in the condensation region disappears. This is a counterexample to a long held conjecture that curvature always diverges in phase transitions.

Suggested Citation

  • Pessoa, Pedro & Cafaro, Carlo, 2021. "Information geometry for Fermi–Dirac and Bose–Einstein quantum statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 576(C).
  • Handle: RePEc:eee:phsmap:v:576:y:2021:i:c:s0378437121003344
    DOI: 10.1016/j.physa.2021.126061
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121003344
    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.2021.126061?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, 2017. "Geometric algebra and information geometry for quantum computational software," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 154-196.
    2. Janke, W. & Johnston, D.A. & Kenna, R., 2004. "Information geometry and phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 181-186.
    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. Cafaro, Carlo, 2017. "Geometric algebra and information geometry for quantum computational software," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 154-196.
    2. Olawale Ayoade & Pablo Rivas & Javier Orduz, 2022. "Artificial Intelligence Computing at the Quantum Level," Data, MDPI, vol. 7(3), pages 1-16, February.
    3. 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.
    4. Fode Zhang & Hon Keung Tony Ng & Yimin Shi & Ruibing Wang, 2019. "Amari–Chentsov structure on the statistical manifold of models for accelerated life tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 77-105, March.
    5. López-Picón, J.L. & López-Vega, J. Manuel, 2021. "Information geometry for the strongly degenerate ideal Bose–Einstein fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    6. Levada Alexandre L., 2016. "Information geometry, simulation and complexity in Gaussian random fields," Monte Carlo Methods and Applications, De Gruyter, vol. 22(2), pages 81-107, June.
    7. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "Information geometry on the curved q-exponential family with application to survival data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 788-802.

    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:576:y:2021:i:c:s0378437121003344. 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.