IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v236y1997i3p296-308.html
   My bibliography  Save this article

From irreversible Markov semigroups to chaotic dynamics

Author

Listed:
  • Antoniou, I.
  • Gustafson, K.

Abstract

We answer qualitatively the inverse coarse-graining problem of statistical physics, namely, which microscopic dynamics give rise to a given physically observed Markov semigroup as a result of exact coarse graining? We prove the fact that all Markov chains arise as projections of dynamical systems in larger spaces and show that in particular the irreversible Markov chains arise as projections of chaotic systems of Kolmogorov type. This result generalizes our previous results on the Misra-Prigogine-Courbage semigroups. Because we want positivity-preserving transformations, our procedure although analogous to the Sz-Nagy-Foias dilation theory has a different viewpoint, that of positive dilations.

Suggested Citation

  • Antoniou, I. & Gustafson, K., 1997. "From irreversible Markov semigroups to chaotic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(3), pages 296-308.
    • Handle: RePEc:eee:phsmap:v:236:y:1997:i:3:p:296-308
    DOI: 10.1016/S0378-4371(96)00375-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437196003755
    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/S0378-4371(96)00375-5?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. Courbage, M. & Coutsomitros, C.Th. & Misra, B., 1989. "Faithfulness property of the transition from Bernoulli systems to irreversible Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(1), pages 167-174.
    2. Jing-Yee, Lee & Tasaki, S., 1992. "Poincaré's theorem and subdynamics for driven systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 59-99.
    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. Antoniou, I. & Gustafson, K. & Suchanecki, Z., 1998. "On the inverse problem of statistical physics: from irreversible semigroups to chaotic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(3), pages 345-361.

    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. Antoniou, Ioannis E. & Prigogine, Ilya, 1993. "Intrinsic irreversibility and integrability of dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(3), pages 443-464.
    2. Antoniou, I. & Melnikov, Yu. & Qiao, Bi, 1997. "Master equation for a quantum system driven by a strong periodic field in the quasienergy representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 97-114.
    3. Bose, Indrani, 1992. "Quantum antiferromagnets with disordered ground states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(1), pages 298-305.

    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:236:y:1997:i:3:p:296-308. 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.