IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v370y2006i2p390-406.html
   My bibliography  Save this article

Phase transitions in small systems: Microcanonical vs. canonical ensembles

Author

Listed:
  • Dunkel, Jörn
  • Hilbert, Stefan

Abstract

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.

Suggested Citation

  • Dunkel, Jörn & Hilbert, Stefan, 2006. "Phase transitions in small systems: Microcanonical vs. canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 390-406.
  • Handle: RePEc:eee:phsmap:v:370:y:2006:i:2:p:390-406
    DOI: 10.1016/j.physa.2006.05.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106006005
    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.2006.05.018?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. Adib, Artur B. & Moreira, André A. & Andrade Jr, José S. & Almeida, Murilo P., 2003. "Tsallis thermostatistics for finite systems: a Hamiltonian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 276-284.
    2. Chomaz, Ph. & Gulminelli, F., 2002. "Generalized definitions of phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 330-335.
    3. Gross, D.H.E., 2002. "Non-extensive Hamiltonian systems follow Boltzmann's principle not Tsallis statistics—phase transitions, Second Law of Thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 99-105.
    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. Matty, Michael & Lancaster, Lachlan & Griffin, William & Swendsen, Robert H., 2017. "Comparison of canonical and microcanonical definitions of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 474-489.
    2. Davis, Sergio & Loyola, Claudia & Peralta, Joaquín, 2023. "Configurational density of states and melting of simple solids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    3. Swendsen, Robert H. & Wang, Jian-Sheng, 2016. "Negative temperatures and the definition of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 24-34.

    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. Vignat, C. & Plastino, A., 2006. "Poincaré's observation and the origin of Tsallis generalized canonical distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 167-172.
    2. Tsallis, Constantino & Borges, Ernesto P. & Plastino, Angel R., 2023. "Entropy evolution at generic power-law edge of chaos," Chaos, Solitons & Fractals, Elsevier, vol. 174(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:370:y:2006:i:2:p:390-406. 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.