IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v654y2024ics037843712400623x.html
   My bibliography  Save this article

On the kinetic temperature of a one-dimensional crystal on the long-time scale

Author

Listed:
  • Lykov, A.A.
  • Murachev, A.S.

Abstract

We investigate the dynamics of the kinetic temperature of a finite one-dimensional harmonic chain, the evolution of which is initiated by a thermal shock. We demonstrate that the kinetic temperature returns arbitrarily close to its initial state (the one immediately following the thermal shock) infinitely many times, and we give an estimate for the time elapsed until the recurrence. This assertion is closely related to the Poincare recurrence theorem and we discuss their relation. To estimate the recurrence time we use its averaging along system’s trajectory and provide a rigorous mathematical definition of the mean recurrence time. It turns out that the mean recurrence time exponentially increases with the number of particles in the chain. A connection is established between this problem and the local theorems of large deviations theory.

Suggested Citation

  • Lykov, A.A. & Murachev, A.S., 2024. "On the kinetic temperature of a one-dimensional crystal on the long-time scale," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 654(C).
    • Handle: RePEc:eee:phsmap:v:654:y:2024:i:c:s037843712400623x
    DOI: 10.1016/j.physa.2024.130114
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712400623X
    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.2024.130114?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:654:y:2024:i:c:s037843712400623x. 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.