On the classical reaction rate and the first-time problems of Brownian motion

Aihua Zhang, Sun Choi

Research output: Contribution to journalArticlepeer-review


We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient (κ) equals to the one (κV) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one (κK) derived by Kramers. We also propose methods for reaction rate determination by analyzing short-time trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates.

Original languageEnglish
Article number128823
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 15 Jul 2023

Bibliographical note

Funding Information:
This work was supported by the Mid-career Researcher Program ( NRF-2020R1A2C2101636 ), Bio & Medical Technology Development Program ( NRF-2022M3E5F3080873 ), Medical Research Center (MRC) grant ( NRF-2018R1A5A2025286 ), and the Brain Pool Program ( NRF-2021H1D3A2A02081370 ) funded by the Ministry of Science and ICT (MSIT) through the National Research Foundation of Korea (NRF) . It was also supported by the Ewha Womans University Research Grant of 2021. We thank T. N. L. Vũ for helpful discussions.

Publisher Copyright:
© 2023 Elsevier B.V.


  • First-time Problems
  • Kramers’ coefficient
  • Langevin equation
  • Reaction rate theory
  • Transition state theory


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