IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v674y2025ics0378437125004388.html
   My bibliography  Save this article

Surprisal analysis of dissipative Fokker-Planck dynamics in phase-space

Author

Listed:
  • Saravanan, Rajendran
  • Levine, R.D.

Abstract

We show that in well-characterized special cases, a maximal entropy-motivated approach can provide an exact description of the dynamics in phase space of a classical dissipative system such as governed by the Fokker-Planck equation. This is achieved by identifying a set of constraints which, when held constant in time, make the system stationary. Even when such a set is not possible in general it can be identified for special limits. An example is a double well potential in the limit of a high barrier between the two wells. Technically we show that the surprisal of the distribution can be expressed as a linear combination of the constraints. The time-dependent expansion coefficients are identified as the Lagrange multipliers needed to impose a distribution of maximal entropy. For an exact solution, the Lagrange multipliers satisfy a closed set of equations of motion. Unlike the reversible case where these equations are linear, the dissipation introduces non-linear terms. Even so, for an exact solution, the equations are integrable. The constraints are a basis for time-dependent constants of the motion. When it is not possible to identify an exact solution the maximal entropy formalism delivers a tight numerical approximation for the distribution. For the Kramers barrier crossing problem for a high barrier, the surprisal analysis correctly determines the branching fraction between the two wells.

Suggested Citation

  • Saravanan, Rajendran & Levine, R.D., 2025. "Surprisal analysis of dissipative Fokker-Planck dynamics in phase-space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
  • Handle: RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125004388
    DOI: 10.1016/j.physa.2025.130786
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437125004388
    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.2025.130786?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:674:y:2025:i:c:s0378437125004388. 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.