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Another way in which a group presence can affect performance is social loafing—the exertion of less effort by a person working together with a group. Social loafing occurs when our individual performance cannot be evaluated separately from the group. Thus, group performance declines on easy tasks (Karau & Williams, 1993). Essentially individual group members loaf and let other group members pick up the slack. Because each individual’s efforts cannot be evaluated, individuals become less...
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Related Experiment Video

Updated: May 11, 2026

Task Interruption and Resumption Paradigm for Testing the Activation and Pursuit of an Abstract Thinking Goal
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Improvements to Kramers turnover theory.

Eli Pollak1, Joachim Ankerhold

  • 1Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel. eli.pollak@weizmann.ac.il

The Journal of Chemical Physics
|May 3, 2013
PubMed
Summary

This study revisits the Kramers turnover problem, analyzing the impact of bath temperature on energy loss. The Mel

Area of Science:

  • Chemical Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • The Kramers turnover problem addresses particle escape rates over potential barriers under external friction.
  • Existing theories by Mel'nikov and Meshkov (MM) and Pollak, Grabert, and Hänggi (PGH) provide solutions but neglect temperature-dependent energy loss.
  • Understanding friction's role in chemical reaction rates and molecular dynamics is crucial.

Purpose of the Study:

  • To analyze the effect of bath temperature on energy loss in the Kramers turnover problem.
  • To investigate the validity of existing theoretical frameworks when temperature dependence is considered.
  • To develop a novel perturbation theory to account for thermal energy exchange with the bath.

Main Methods:

  • Application of a novel perturbation theory to analyze energy loss mechanisms.

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  • Comparison of theoretical predictions with the Mel'nikov and Meshkov (MM) and Pollak, Grabert, and Hänggi (PGH) formulations.
  • Analysis of a cubic potential with Ohmic friction.

    • Main Results:

    • The Mel'nikov and Meshkov (MM) approach exhibits a divergence in thermal energy gain, indicating a theoretical failure.
    • The Pollak, Grabert, and Hänggi (PGH) approach shows a minor, finite reduction in energy loss with increasing bath temperature.
    • The PGH theory remains largely unaffected by the temperature dependence of energy loss.

    Conclusions:

    • The MM theory's inability to account for temperature-dependent energy loss highlights its limitations.
    • The PGH theory demonstrates greater robustness in describing particle escape rates across varying bath temperatures.
    • This work provides a more refined understanding of friction and temperature effects in barrier crossing phenomena.