IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v215y1995i3p339-360.html
   My bibliography  Save this article

Maximum information entropy approach to non-markovian random jump processes with long memory: application to surprisal analysis in molecular dynamics

Author

Listed:
  • Ovidiu Vlad, Marcel
  • Mackey, Michael C.

Abstract

It is shown that non-markovian random jump processes in continuous time and with discrete state variables can be expressed in terms of a variational principle for the information entropy provided that the constraints describe the correlations among a set of dynamic variables at any moment in the past. The approach encompasses a broad class of stochastic processes ranging from independent processes through markovian and semi-markovian processes to random processes with complete connections. Two different levels of description are introduced: (a) a microscopic one defined in terms of a set of microscopic state variables; and (b) a mesoscopic one which gives the stochastic properties of the dynamic variables in terms of which the constrains are defined. A stochastic description of both levels is given in terms of two different characteristic functionals which completely characterize the fluctuations of micro- and mesovariables. At the mesoscopic level a statistic-thermodynamic description is also possible in terms of a partition functional. The stochastic and thermodynamic descriptions of the mesoscopic level are equivalent and the comparison between these two approaches leads to a generalized fluctuation-dissipation relation. A comparison is performed between the maximum entropy and the master equation approaches to non-markovian processes. A system of generalized age-dependent master equations is derived which provides a description of stochastic processes with long memory. The general approach is applied to the problem of surprisal analysis in molecular dynamics. It is shown that the usual markovian master-equation description is compatible with the information entropy approach provided that the constraints give the evolution of the first two moments of the dynamic variables at any time in the past.

Suggested Citation

  • Ovidiu Vlad, Marcel & Mackey, Michael C., 1995. "Maximum information entropy approach to non-markovian random jump processes with long memory: application to surprisal analysis in molecular dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(3), pages 339-360.
  • Handle: RePEc:eee:phsmap:v:215:y:1995:i:3:p:339-360
    DOI: 10.1016/0378-4371(94)00269-Y
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719400269Y
    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/10.1016/0378-4371(94)00269-Y?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Davies, J. & Mabin, V.J. & Balderstone, S.J., 2005. "The theory of constraints: a methodology apart?--a comparison with selected OR/MS methodologies," Omega, Elsevier, vol. 33(6), pages 506-524, December.
    2. Huber, D.L. & Vlad, M.O., 1997. "Statistical model for stretched exponential relaxation with backtransfer and leakage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 81-89.

    More about this item

    Statistics

    Access and download statistics

    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:215:y:1995:i:3:p:339-360. 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.