IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v513y2019icp497-509.html
   My bibliography  Save this article

Irreversibility from staircases in symplectic embeddings

Author

Listed:
  • Creaco, Anthony J.
  • Kalogeropoulos, Nikolaos

Abstract

We present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of Hamiltonian systems of many degrees of freedom. We use recent flexibility and rigidity results of symplectic embeddings, quantified via the (stabilized) Fibonacci and Pell staircases, to encode the underlying breadth of the possible initial conditions, which alongside the multitude of degrees of freedom of the underlying system give rise to time-irreversibility.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:497-509
    DOI: 10.1016/j.physa.2018.09.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118311798
    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.2018.09.047?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. Lebowitz, Joel L., 1999. "Microscopic origins of irreversible macroscopic behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 516-527.
    2. Kalogeropoulos, Nikolaos, 2018. "Time irreversibility from symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 202-210.
    3. Kalogeropoulos, Nikos, 2012. "Tsallis entropy induced metrics and CAT(k) spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3435-3445.
    4. Zakharov, A.Yu., 2017. "Determinism vs. statistics in classical many-body theory: Dynamical origin of irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 72-76.
    5. Cerino, L. & Cecconi, F. & Cencini, M. & Vulpiani, A., 2016. "The role of the number of degrees of freedom and chaos in macroscopic irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 486-497.
    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. Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Kalogeropoulos, Nikolaos, 2022. "Coarse-graining and symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(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. Lebed, Igor V., 2019. "The cause for emergence of irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 325-341.
    2. Kalogeropoulos, Nikolaos, 2018. "Time irreversibility from symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 202-210.
    3. Gorban, Alexander, 2007. "Order–disorder separation: Geometric revision," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 85-102.
    4. Balankin, Alexander S. & Bory-Reyes, Juan & Shapiro, Michael, 2016. "Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 345-359.
    5. Zakharov, A.Yu., 2019. "On physical principles and mathematical mechanisms of the phenomenon of irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1289-1295.
    6. 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.
    7. Kalogeropoulos, Nikolaos, 2022. "Coarse-graining and symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    8. Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    9. Baldovin, Marco & Caprini, Lorenzo & Vulpiani, Angelo, 2019. "Irreversibility and typicality: A simple analytical result for the Ehrenfest model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 422-429.
    10. 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.
    11. 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.

    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:513:y:2019:i:c:p:497-509. 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.