IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v247y1997i1p338-356.html
   My bibliography  Save this article

Rates and mean first passage times

Author

Listed:
  • Müller, Reinhard
  • Talkner, Peter
  • Reimann, Peter

Abstract

The relation between mean first passage times T and transition rates Γ in noisy dynamical systems with metastable states is investigated. It is shown that the inverse mean first passage time to the separatrix of the noiseless system may deviate from twice the rate not only because in general the deterministic separatrix is not the locus in the state space from which a noisy trajectory goes to either side with equal probability. A further cause of a deviation from the often assumed relation ΓT = 12 between rates and mean first passage times is given if the noisy dynamics is discontinuous, i.e. shows jumps with finite probability. Then the value of the splitting probability at the separatrix does not fix the value of ΓT since the system need not visit the separatrix during a transition from one to the other side. Most important, for discontinuous processes the deviation from the ΓT = 12 rule survives even in the weak noise limit. A mathematical relation for the product of the rate and the mean first passage time is proposed for Markovian processes and numerically confirmed for a particular one-dimensional noisy map.

Suggested Citation

  • Müller, Reinhard & Talkner, Peter & Reimann, Peter, 1997. "Rates and mean first passage times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 247(1), pages 338-356.
    • Handle: RePEc:eee:phsmap:v:247:y:1997:i:1:p:338-356
    DOI: 10.1016/S0378-4371(97)00390-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437197003907
    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(97)00390-7?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. Kummel, Reiner & Schussler, Uwe, 1991. "Heat equivalents of noxious substances: a pollution indicator for environmental accounting," Ecological Economics, Elsevier, vol. 3(2), pages 139-156, July.
    2. C. Knessl & B. J. Matkowsky & Z. Schuss & C. Tier, 1990. "An Integral Equation Approach to the M/G/2 Queue," Operations Research, INFORMS, vol. 38(3), pages 506-518, June.
    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. Berezhkovskii, A.M. & Zitserman, V.Yu., 1992. "Multidimensional activated rate processes with slowly relaxing mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(3), pages 519-550.
    2. Roma, Antonio & Pirino, Davide, 2009. "The extraction of natural resources: The role of thermodynamic efficiency," Ecological Economics, Elsevier, vol. 68(10), pages 2594-2606, August.
    3. Huesemann, Michael H., 2001. "Can pollution problems be effectively solved by environmental science and technology? An analysis of critical limitations," Ecological Economics, Elsevier, vol. 37(2), pages 271-287, May.
    4. Sollner, Fritz, 1997. "A reexamination of the role of thermodynamics for environmental economics," Ecological Economics, Elsevier, vol. 22(3), pages 175-201, September.
    5. Rebane, Karl K., 1995. "Energy, entropy, environment: why is protection of the environment objectively difficult?," Ecological Economics, Elsevier, vol. 13(2), pages 89-92, May.

    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:247:y:1997:i:1:p:338-356. 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.