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Reaction-rate theory: fifty years after Kramers

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Hänggi, Peter, Talkner, Peter, Borkovec, Michal·1990·Reviews of Modern Physics
DOI 10.1103/revmodphys.62.251
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Abstract

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

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  • The phenomenological rate law applies only after a characteristic time τ_c in which the transient phase has ended.

    “The phenomenological rate law applies only after a characteristic time τ c in which this transient phase has ended.”

    From An open quantum systems approach to proton tunnelling in DNA (2022) · cites this paper as [35]

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Authors
Hänggi, P., Talkner, P., & Borkovec, M.
Affiliations
University of Augsburg (DE)
ORCID
Borkovec, Michal
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
1990-04-01
Volume
62
Issue
2
Pages
251-341
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.62.251
OpenAlex
W2092144432
Cited by
6,154
References
619
Citations by year
2026: 187 · 2025: 193 · 2024: 200 · 2023: 192 · 2022: 231 · 2021: 248 · 2020: 235 · 2019: 165 · 2018: 213 · 2017: 219 · 2016: 196 · 2015: 209 · 2014: 256 · 2013: 196 · 2012: 222
FWCI
71.83
Type
journal article
Language
en
Open access
Licence
Locations
  • Reviews of Modern Physics (publishedVersion)
  • DORA PSI (Paul Scherrer Institute) (submittedVersion, other-oa)
  • Publication Server of Goethe University Frankfurt am Main (Goethe University Frankfurt) (submittedVersion)
  • OPUS (Augsburg University) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
Keywords
metastable systems, transition state theory, turnover theory, mean first passage time, driven systems, quantum tunneling, rate constants

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