IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v634y2024ics0378437123009792.html
   My bibliography  Save this article

Perturbation theory in a microcanonical ensemble

Author

Listed:
  • Pradhan, Ritapriya
  • Bhattacharjee, Jayanta K.

Abstract

The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, mainly the canonical and grand canonical ensembles have been used. In this article we show how the microcanonical ensemble can be directly used to carry out perturbation theory for both non-interacting and interacting systems. We obtain the first non-trivial order answers for the specific heat of anharmonic oscillators and for the virial expansion in real gases. They are in exact agreement with the results obtained from the canonical ensemble. In addition, we show how crossover functions for the specific heat of anharmonic oscillators can be constructed using a microcanonical ensemble and also how the subsequent terms of the virial expansion can be obtained. We find that if we consider quantum free particles in a one-dimensional box of extension L, then both the ensembles give an unusual result for the first correction to the specific heat in the high temperature limit.

Suggested Citation

  • Pradhan, Ritapriya & Bhattacharjee, Jayanta K., 2024. "Perturbation theory in a microcanonical ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    • Handle: RePEc:eee:phsmap:v:634:y:2024:i:c:s0378437123009792
    DOI: 10.1016/j.physa.2023.129424
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123009792
    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.2023.129424?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. Nicole Yunger Halpern & Philippe Faist & Jonathan Oppenheim & Andreas Winter, 2016. "Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges," Nature Communications, Nature, vol. 7(1), pages 1-7, November.
    2. Lynden-Bell, D., 1999. "Negative specific heat in astronomy, physics and chemistry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 293-304.
    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. Palma-Chilla, L. & Flores, J.C., 2017. "Negative heat capacity in a left-handed system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 396-401.
    2. Casetti, Lapo & Kastner, Michael, 2007. "Partial equivalence of statistical ensembles and kinetic energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 318-334.
    3. Shayan Majidy, 2024. "Noncommuting charges can remove non-stationary quantum many-body dynamics," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    4. F. H. B. Somhorst & R. Meer & M. Correa Anguita & R. Schadow & H. J. Snijders & M. Goede & B. Kassenberg & P. Venderbosch & C. Taballione & J. P. Epping & H. H. Vlekkert & J. Timmerhuis & J. F. F. Bul, 2023. "Quantum simulation of thermodynamics in an integrated quantum photonic processor," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    5. Touchette, Hugo & Ellis, Richard S. & Turkington, Bruce, 2004. "An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 138-146.
    6. Zamora, D.J. & Rocca, M.C. & Plastino, Angel, 2020. "Statistical Mechanics of planar stellar systems: Solving divergences in self-gravitational systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    7. Ellis, Richard S. & Touchette, Hugo & Turkington, Bruce, 2004. "Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume–Emery–Griffiths model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 518-538.
    8. Bouchet, Freddy & Gupta, Shamik & Mukamel, David, 2010. "Thermodynamics and dynamics of systems with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4389-4405.
    9. Mirtorabi, M. & Miraboutalebi, S. & Masoudi, A.A. & Matin, L. Farhang, 2020. "Some thermodynamics modifications by the least length assumption via the microcanonical scheme," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

    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:634:y:2024:i:c:s0378437123009792. 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.