The DOI matches its Crossref record; 619 of the 619 references it cites were found in a registry or an index.
Reaction-rate theory: fifty years after Kramers
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A unified formulation of the constant temperature molecular dynamics methods
Nosé, S. (1984) · The Journal of Chemical Physics · doi:10.1063/1.447334 · Cited by 17,163
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
Einstein, A., Podolsky, B., & Rosen, N. (1935) · Physical Review · doi:10.1103/physrev.47.777 · Cited by 16,654
Quantum Mechanics and Path Integrals
Miguel Blasco, L. D. (1966) · Students Quarterly Journal · doi:10.1049/sqj.1966.0063 · Cited by 9,884
Kubo, R. (1957) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.12.570 · Cited by 9,441
Risken, H. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-61544-3 · Cited by 9,128
Table of Integrals, Series and Products.
L., Y., Gradshteyn, I. S., & RYZHIK, I. M. (1981) · Mathematics of Computation · doi:10.2307/2007757 · Cited by 8,970
Einstein, A. (1905) · Annalen der Physik · doi:10.1002/andp.19053220806 · Cited by 8,762
Brownian motion in a field of force and the diffusion model of chemical reactions
Kramers, H. A. (1940) · Physica · doi:10.1016/s0031-8914(40)90098-2 · Cited by 8,561
Stochastic Problems in Physics and Astronomy
Chandrasekhar, S. (1943) · Reviews of Modern Physics · doi:10.1103/revmodphys.15.1 · Cited by 8,537
Reciprocal Relations in Irreversible Processes. I.
Onsager, L. (1931) · Physical Review · doi:10.1103/physrev.37.405 · Cited by 6,660
Research works printed but not linked: 111
- Abraham, F. F., 1974, Homogeneous Nucleation
- Agarwal, G. S., 1974, Quantum Optics, Springer Tracts in Modern Physics Vol. 70
- Alberding, N., 1978, Hydrogen in Metals
- Alicki, R., 1987, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics Vol. 286
- Andronov, A. A., 1966, Theory of Oscillations
- Arrhenius, S., 1889, Z. Phys. Chem. (Leipzig), 4, 226, 10.1515/zpch-1889-0416 · DOI
- Bernasconi, J., 1985, Helv. Phys. Acta, 58, 597
- Berne, B. J., 1985, Multiple Time Scales
- Berne, B. J., 1970, Adv. Chem. Phys., 17, 63
- Bernoulli, D., 1732, Commentarii Academiae Scientiarum Imperialis Petropolitanae, 6, 108
- Bernoulli, D., 1734, Commentarii Academiae Scientiarum Imperials Petropolitanae, 7, 162
- Berry, R. S., 1980, Physical Chemistry
- Binder, K., 1986, Topics in Current Physics No. 7
- Bohr, A., 1969, Nuclear Structure
- Borkovec, M., 1990, J. Chem. Phys.
- Caldeira, A. O., Ann. Phys. (N.Y.), 153, 445
- Caldeira, A. O., Physica A (Utrecht), 130, 374
- Callear, A. B., 1983, Modern Methods in Kinetics, Comprehensive Chemical Kinetics
- Careri, G., 1989, Dissipative Quantum Tunneling of Protons on Hydrated Protein Powders
- Dmitrenko, I. M., 1985, Fiz. Nizk. Temp., 11, 146
- Dogonadze, R. R., 1970, Teor. Eksp. Khim., 6, 298
- Farina, J. D., 1981, Optical Bistability I
- Feller, W., 1966, Introduction to Probability and Its Application
- Fokker, A. D., 1914, Ann. Phys. (Leipzig), 43, 812
- Fonseca, T., 1985, Adv. Chem. Phys., 62, 389
- Forster, D., 1975, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions, Frontiers in Physics
- Glasstone, S., 1941, The Theory of Rate Processes
- Goldanskii, V. I., 1959, Dokl. Acad. Nauk SSSR, 124, 1261
- Goldanskii, V. I., 1959, Dokl. Acad. Nauk SSSR, 127, 1037
- Goldanskii, V. I., 1987, Sov. Sci. Rev. Chem. B, 9, 59
- Goldstein, H., 1980, Classical Mechanics
- Grabert, H., 1985, SQUID 85
- Grabert, H., 1986, Tunneling
- Grigolini, P., 1985, Adv. Chem. Phys., 62, 29
- Gross, D. H. E., 1980, Deep Inelastic and Fusion Reactions with Heavy Ions, Lecture Notes in Physics No. 117
- Haake, F., 1973, Statistical Treatment of Open Systems by Generalized Master Equations, Springer Tracts in Modern Physics Vol. 66
- Hynes, J. T., 1988, Discuss. Faraday Soc., 85, 353
- Iansiti, M., 1989, APS March Meeting, St. Louis
- Iansiti, M., Bull. Am. Phys. Soc., 562
- Iansiti, M., Bull. Am. Phys. Soc.
- Jauslin, H., 1986, Tunneling
- Klein, O., 1922, Ark. Mat. Astron. Fys., 16, 1
- Klyatskin, V. I., 1977, Radiofizika, 20, 562
- Korshunov, S. E., 1987, Zh. Eksp. Teor. Fiz., 92, 1828
- Kubo, R., 1959, Lectures in Theoretical Physics, Boulder
- Laidler, K. J., 1987, Chemical Kinetics
- Landau, L., 1932, Phys. Z. Sowjetunion, 1, 89
- Langer, J. S., 1980, Systems Far from Equilibrium, Lecture Notes in Physics Vol. 132
- Larkin, A. I., 1983, Pis'ma Zh. Eksp. Teor. Fiz., 37, 322
- Larkin, A. I., 1984, Zh. Eksp. Teor. Fiz., 86, 719
- Laue, M., 1918, Jahrb. Radiakt. Elektron., 15, 205
- Laue, M., Jahrb. Radiakt. Elektron., 15, 257
- Laue, M., Jahrb. Radiakt. Elektron., 15, 301
- Lefevre-Seguin, V., 1990, Thermally-Activated Escape of D.C. Squids at 4.2 K: A New Confirmation of the Kramers Theory in Two Dimensions
- Lett, P., 1986, Optical Instabilities, Cambridge Studies in Modern Optics Vol. 4
- Lewis, G. N., 1925, J. Am. Chem. Soc., 47, 1514
- Lichtenberg, A. J., 1983, Appl. Math. Sci.
- Mandel, L., 1981, Optical Bistability I
- Marchesoni, F., 1990, Pair Production in a φ4-String
- Melnikov, V. I., 1984, Zh. Eksp. Teor. Fiz., 87, 663
- Melnikov, V. I., 1983, Pis'ma Zh. Eksp. Teor. Fiz., 38, 111
- Montroll, E. W., 1958, Adv. Chem. Phys., 1, 361
- Moss, F., 1989, Noise in Nonlinear Dynamical Systems
- Nikitin, E. E., 1966, Theory of Thermally Induced Gas Phase Reactions
- Nikitin, E. E., 1974, Physical Chemistry: An Advanced Treatise
- Nitzan, A., 1988, Adv. Chem. Phys., 70, 489
- Oppenheimer, J. R., 1928, Phys. Rev., 31, 80
- Ornstein, L. S., 1917, Versl. Acad. Amst., 26, 1005
- Ornstein, L. S., 1919, Proc. Acad. Amst., 21, 96
- Petukhov, B. V., 1972, Zh. Eksp. Teor. Fiz., 63, 634
- Pfeifer, P., 1983, Symmetries and Properties of Nonrigid Molecules: A Comprehensive Survey
- Pirc, R., 1969, Phys. Kondens. Mater., 9, 377
- Planck, M., 1917, Sitzungsber. Preuss. Akad. Wiss., 324
- Pollak, E., 1985, Theory of Chemical Reaction Dynamics
- Pollak, E., 1990, J. Chem. Phys.
- Pontryagin, L. A., 1933, Zh. Eksp. Teor. Fiz., 3, 165
- J. B. Barbour, 1989, Noise in Nonlinear Dynamics
- Primas, H., 1978, Adv. Chem. Phys., 38, 1
- Rayleigh, Lord, 1902, Scientific Papers of Lord Rayleigh
- Reimann, P., 1989, Stationary Probability for one-dimensional Discrete Maps disturbed by weak Gaussian Noise
- Rice, O. K., 1930, Z. Phys. Chem. Abt. B, 7, 226
- Richardson, O. W., 1902, Proc. Cambridge Philos. Soc., 11, 286
- Richter, D., 1987, Quantum Aspects of Molecular Motion in Solids
- Rips, I., 1990, Phys. Rev. A
- Roy, R., 1989, Noise in Nonlinear Dynamical Systems
- Sargent, M., 1974, Laser Physics
- Sceats, M. G., 1988, Adv. Phys. Chem., 70, 357
- Schrödinger E., 1915, Phys. Z., 16, 289
- Seeger, A., 1966, Physical Acoustics
- Sinha, K., 1972, Helv, Phys. Acta, 45, 619
- Smoluchowski, M. V., 1914, Bull. Acad. Cracovie, Classe des sciences mathématiques et naturelles, Serie A, 418
- Smoluchowski, M. V., 1915, Ann. Phys. (Leipzig), 48, 1103
- Smoluchowski, M. V., 1917, Z. Phys. Chem. (Leipzig), 92, 129
- Stiller, W., 1989, Arrhenius Equation and Nonequilibrium Kinetics, Teubner Texte zur Physik Bd. 21
- Stillinger, F. H., 1978, Theor. Chem., 3, 178
- Stratonovich, R. L., 1963, Topics in the Theory of Random Noise
- Stückelberg, E. G. C., 1932, Helv. Phys. Acta, 5, 369
- Sussmann, J. A., 1971, Ann. Phys. (Paris), 6, 135
- Talkner, P., 1989, Helv. Phys. Acta, 62, 932
- Talkner, P., 1983, Noise in Physical Systems and 1f Noise
- Tikhonov, V. I., 1960, Avtomatika i Telemekhanika, 21, 301
- O. M. Blunn, 1965, Nonlinear Transformations of Stochastic Processes
- Troe, J., 1975, Physical Chemistry: An Advanced Treatise
- Uhlhorn, U., 1960, Ark. Fys., 17, 361
- Van Kampen, N. G., 1976, Adv. Chem. Phys., 34, 245
- Velsko, S. P., 1982, J. Chem. Phys., 65, 59
- Wardlaw, D. W., 1988, Adv. Chem. Phys., 70, 231
- Weiss, G. H., 1983, Adv. Chem. Phys., 32, 363
- Weiss, U., 1980, Functional Integration: Theory and Application
- Weiss, U., Phys. Lett. A, 104, 492
- Zeldovich, Ya. B., 1943, Acta Phys. Chim. USSR, 18, 1
Cited by
Sorted by citations
Items 801–900 of 1,003
Barriers in protein folding reactions
Bilsel, O., & Matthews, C. R. (2000) · Advances in protein chemistry · doi:10.1016/s0065-3233(00)53004-6 · Cited by 72
Current and universal scaling in anomalous transport
Goychuk, I., Heinsalu, E., Patriarca, M., Schmid, G., & Peter Hänggi, A. (2006) · Physical Review E · doi:10.1103/physreve.73.020101 · Cited by 72
Brownian parametric quantum oscillator with dissipation
Zerbe, C., & Peter Hänggi, A. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.52.1533 · Cited by 72
Rabani, E., Krilov, G., & Berne, B. J. (2000) · The Journal of Chemical Physics · doi:10.1063/1.480834 · Cited by 72
Rate Theory for Correlated Processes: Double Jumps in Adatom Diffusion
Jacobsen, J., Jacobsen, K. W., & Sethna, J. P. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.2843 · Cited by 71
Filling the Voids of Graphene Foam with Graphene “Eggshell” for Improved Lithium-Ion Storage
Goh, B.-M., Wang, Y., Reddy, M. V., Ding, Y. L., Lü, L., Bunker, C. E., & Loh, K. P. (2014) · ACS Applied Materials & Interfaces · doi:10.1021/am5022655 · Cited by 71
Grebenkov, D. S., Metzler, R., & Oshanin, G. (2019) · publish.UP (University of Potsdam) · doi:10.25932/publishup-42298 · Cited by 71
Escape dynamics of active particles in multistable potentials
Militaru, A., Innerbichler, M., Frimmer, M., Tebbenjohanns, F., Novotný, L., & Dellago, C. (2021) · Nature Communications · doi:10.1038/s41467-021-22647-6 · Cited by 71
Computational Models of the Notch Network Elucidate Mechanisms of Context-dependent Signaling
Agrawal, S., Archer, C. T., & Schaffer, D. V. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000390 · Cited by 71
Incipient plasticity and dislocation nucleation in body-centered cubic chromium
Wu, D., & Nieh, T. G. (2014) · Materials Science and Engineering A · doi:10.1016/j.msea.2014.04.107 · Cited by 71
Stretched exponentials and barrier distributions
Edholm, O., & Blomberg, C. (2000) · Chemical Physics · doi:10.1016/s0301-0104(99)00349-3 · Cited by 71
Anomalous transport in biased ac-driven Josephson junctions: Negative conductances
Kostur, M., Machura, Ł., Peter Talkner, A., Peter Hänggi, A., & Łuczka, J. (2008) · Physical Review B · doi:10.1103/physrevb.77.104509 · Cited by 71
The non-Arrhenius migration of interstitial defects in bcc transition metals
Dudarev, S. L. (2008) · Comptes Rendus Physique · doi:10.1016/j.crhy.2007.09.019 · Cited by 71
First exit times of harmonically trapped particles: a didactic review
Grebenkov, D. S. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/1/013001 · Cited by 71
Transition state theory in liquids beyond planar dividing surfaces
Hernandez, R., Uzer, T., & Bartsch, T. (2010) · Chemical Physics · doi:10.1016/j.chemphys.2010.01.016 · Cited by 71
A Primer on Noise-Induced Transitions in Applied Dynamical Systems
Forgoston, E., & Moore, R. O. (2018) · SIAM Review · doi:10.1137/17m1142028 · Cited by 71
Bacteria as living patchy colloids: Phenotypic heterogeneity in surface adhesion
Vissers, T., Brown, A. T., Koumakis, N., Dawson, A., Hermes, M., Schwarz‐Linek, J., Schofield, A. B., French, J. M., Koutsos, V., Arlt, J., et al. (2018) · Science Advances · doi:10.1126/sciadv.aao1170 · Cited by 66
Microscopic model of carbon monoxide binding to myoglobin
McMahon, B. H., Stojković, B. P., Hay, P. J., Martin, R. L., & Garcı́a, A. E. (2000) · The Journal of Chemical Physics · doi:10.1063/1.1309524 · Cited by 71
Spatial dependence of time-dependent friction for pair diffusion in a simple fluid
Straub, J. E., Berne, B. J., & Roux, B. (1990) · The Journal of Chemical Physics · doi:10.1063/1.458950 · Cited by 71
Stochastic simulation of quantum dissipative dynamics
Zhou, Y., Yan, Y., & Shao, J. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10262-4 · Cited by 71
Efficient dynamic importance sampling of rare events in one dimension
Zuckerman, D. M., & Woolf, T. B. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.63.016702 · Cited by 71
The Estimates of the Mean First Exit Time of a Bistable System Excited by Poisson White Noise
Xu, Y., Li, H., Wang, H., Jia, W., Yue, X., & Kurths, J. (2017) · Journal of Applied Mechanics · doi:10.1115/1.4037158 · Cited by 70
Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable systems
Alfonsi, L., Gammaitoni, L., Santucci, S., & Bulsara, A. R. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.299 · Cited by 70
Large deviation function for entropy production in driven one-dimensional systems
Mehl, J., Speck, T., & Seifert, U. (2008) · Physical Review E · doi:10.1103/physreve.78.011123 · Cited by 70
Intramolecular Diels−Alder Reaction in Ionic Liquids: Effect of Ion-Specific Solvent Friction
Tiwari, S. S., Khupse, N. D., & Kumar, A. (2008) · The Journal of Organic Chemistry · doi:10.1021/jo801802q · Cited by 70
Xie, S., & Schweizer, K. S. (2016) · Macromolecules · doi:10.1021/acs.macromol.6b02272 · Cited by 70
Neglected adsorbate interactions behind diffusion prefactor anomalies on metals
Ovesson, S., Bogicevic, A., Wahnström, G., & Lundqvist, B. I. (2001) · Physical review. B, Condensed matter · doi:10.1103/physrevb.64.125423 · Cited by 70
Quantum dynamics in strong fluctuating fields
Goychuk, I., & Hänggi, P. (2005) · Advances In Physics · doi:10.1080/00018730500429701 · Cited by 70
Self-citationTransition pathways in a many-body system: Application to hydrogen-bond breaking in water
Csajka, F. S., & Chandler, D. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476656 · Cited by 70
Quantum nucleation of vortices in the flow of superfluid He4 through an orifice
Ihas, G. G., Avenel, O., Aarts, R. G. K. M., Salmelin, R. H., & Varoquaux, E. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.327 · Cited by 70
Hydrodynamically Enforced Entropic Trapping of Brownian Particles
Martens, S., Straube, A. V., Schmid, G., Schimansky-Geier, L., & Peter Hänggi, A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.010601 · Cited by 69
Mechanical Modulation of Receptor-Ligand Interactions at Cell-Cell Interfaces
Allard, J. F., Dushek, O., Coombs, D., & van der Merwe, P. A. (2012) · Biophysical Journal · doi:10.1016/j.bpj.2012.02.006 · Cited by 68
Surmounting oscillating barriers: Path-integral approach for weak noise
Lehmann, J., Reimann, P., & Peter Hänggi, A. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.6282 · Cited by 69
Zhou, Y., Pearson, J. E., & Auerbach, A. L. (2005) · Biophysical Journal · doi:10.1529/biophysj.105.067215 · Cited by 69
Fractures in complex fluids: the case of transient networks
Ligoure, C., & Mora, S. (2013) · Rheologica Acta · doi:10.1007/s00397-012-0668-0 · Cited by 70
Unified Model of Dynamic Forced Barrier Crossing in Single Molecules
Friddle, R. W. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.138302 · Cited by 69
Dispersionless Transport in a Washboard Potential
Lindenberg, K., Sancho, J. M., Palacio, A. M. L., & Sokolov, I. M. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.020602 · Cited by 69
Enhancement of reaction rate in small-sized droplets: A combined analytical and simulation study
Mondal, S., Acharya, S., Biswas, R., Bagchi, B., & Zare, R. N. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5030114 · Cited by 70
Mesoscopic model for diffusion-influenced reaction dynamics
Tucci, K., & Kapral, R. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1690244 · Cited by 69
Models of chemical reactions with participation of polymers
Oshanin, G., Moreau, M., & Burlatsky, S. F. (1994) · Advances in Colloid and Interface Science · doi:10.1016/0001-8686(94)80011-1 · Cited by 69
Relativistic diffusion processes and random walk models
Dunkel, J., Peter Talkner, A., & Peter Hänggi, A. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.043001 · Cited by 69
A multiscale cohesive zone model for rate-dependent fracture of interfaces
Yang, T., Liechti, K. M., & Huang, R. (2020) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2020.104142 · Cited by 68
Nonlinearity-Induced Nonreciprocity—Part I
Cotrufo, M., Mann, S. A., Moussa, H., & Alù, A. (2021) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2021.3079250 · Cited by 68
Theory of the structural glass transition: a pedagogical review
Lubchenko, V. (2015) · Advances In Physics · doi:10.1080/00018732.2015.1057979 · Cited by 67
Tunneling in hydrogen and deuterium atom addition to CO at low temperatures
Andersson, S., Goumans, T. P. M., & Arnaldsson, A. (2011) · Chemical Physics Letters · doi:10.1016/j.cplett.2011.07.073 · Cited by 68
On detailed balance and reversibility of semi-Markov processes and single-molecule enzyme kinetics
Wang, H., & Qian, H. (2007) · Journal of Mathematical Physics · doi:10.1063/1.2432065 · Cited by 68
Angelani, L. (2015) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/49/495003 · Cited by 68
A Review of Enhanced Sampling Approaches for Accelerated Molecular Dynamics
Tiwary, P., & van de Walle, A. (2016) · Springer series in materials science · doi:10.1007/978-3-319-33480-6_6 · Cited by 67
Two-State Theory of Nonlinear Stochastic Resonance
Casado‐Pascual, J., Gómez-Ordóñez, J., Morillo, M., & Peter Hänggi, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.210601 · Cited by 68
Mechanism and free-energy barrier of the type-57 reconstruction of the zigzag edge of graphene
Kroes, J. M. H., Akhukov, M. A., Los, J. H., Pineau, N., & Fasolino, A. (2011) · Physical Review B · doi:10.1103/physrevb.83.165411 · Cited by 67
Designing self-assembling kinetics with differentiable statistical physics models
Goodrich, C. P., King, E. M., Schoenholz, S. S., Cubuk, E. D., & Brenner, M. P. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2024083118 · Cited by 71
Modelling and computation of liquid crystals
Wang, W. A., Zhang, L., & Zhang, P. (2021) · Acta Numerica · doi:10.1017/s0962492921000088 · Cited by 67
Ahmad, K., Rizzi, A., Capelli, R., Mandelli, D., Lyu, W., & Carloni, P. (2022) · Frontiers in Molecular Biosciences · doi:10.3389/fmolb.2022.899805 · Cited by 66
Reaction-rate theory with account of the crystal anharmonicity
Dubinko, V. I., Selyshchev, P. A., & Archilla, J. F. R. (2011) · Physical Review E · doi:10.1103/physreve.83.041124 · Cited by 67
MD Simulation of Protein-Ligand Interaction: Formation and Dissociation of an Insulin-Phenol Complex
Swegat, W., Schlitter, J., Krüger, P., & Wollmer, A. (2003) · Biophysical Journal · doi:10.1016/s0006-3495(03)74962-5 · Cited by 67
Linear viscoelastic behavior of aggregated colloidal dispersions
Wolthers, W., van den Ende, D., Breedveld, V., Duits, M. H. G., Potanin, A. A., Wientjes, R. H. W., & Mellema, J. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.56.5726 · Cited by 67
The transition state transit time of WW domain folding is controlled by energy landscape roughness
Liu, F., Nakaema, M. K. K., & Gruebele, M. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3262489 · Cited by 67
Peters, B. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3271024 · Cited by 65
Popa, I., Fernández, J. M., & Garcia-Manyes, S. (2011) · Journal of Biological Chemistry · doi:10.1074/jbc.m111.264093 · Cited by 67
Schmitt, C., Nadtochy, P. N., Heinz, A., Jurado, B., Kelić, A., & Schmidt, K. ‐. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.042701 · Cited by 67
Ghysels, A., Venable, R. M., Pastor, R. W., & Hummer, G. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00039 · Cited by 67
Ma, C., Ji, T., Robertson, C. G., Rajeshbabu, R., Zhu, J., & Dong, Y. (2017) · Physical Chemistry Chemical Physics · doi:10.1039/c7cp01142c · Cited by 66
Satija, R., Das, A., & Makarov, D. E. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4993228 · Cited by 67
A pseudo-elasticity theory to model the strain-softening behavior of tough hydrogels
Lu, T., Wang, Z., Tang, J., Zhang, W., & Wang, T. (2019) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2019.103832 · Cited by 66
Stochastic dynamics of time correlation in complex systems with discrete time
Yulmetyev, R. M., Peter Hänggi, A., & Gafarov, F. M. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.6178 · Cited by 67
Saltzman, E. J., & Schweizer, K. S. (2006) · Physical Review E · doi:10.1103/physreve.74.061501 · Cited by 67
Oscillatory systems driven by noise: Frequency and phase synchronization
Callenbach, L., Peter Hänggi, A., Linz, S. J., Freund, J. A., & Schimansky-Geier, L. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.051110 · Cited by 67
Yan, Y., Xing, T., & Shi, Q. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0027962 · Cited by 66
On the Thermal Models for Resistive Random Access Memory Circuit Simulation
Roldán, J. B., González-Cordero, G., Picos, R., Miranda, E. A., Palumbo, F., Jiménez-Molinos, F., Moreno, E., Maldonado, D., Boyeras, S., Chawa, M. M. A., et al. (2021) · Nanomaterials · doi:10.3390/nano11051261 · Cited by 66
Protein dynamics underlying allosteric regulation
Astore, M. A., Pradhan, A. S., Thiede, E. H., & Hanson, S. M. (2024) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2023.102768 · Cited by 64
Soft Lattice and Phase Stability of α‐FAPbI 3
Kim, H., & Park, N. (2024) · Advanced Energy Materials · doi:10.1002/aenm.202400089 · Cited by 66
Stochastic system with coupling between non-Gaussian and Gaussian noise terms
Wu, D., Luo, X., & Zhu, S. (2006) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2006.02.049 · Cited by 66
Luo, Y., Utecht, M., Dokić, J., Korchak, S. E., Vieth, H., Haag, R., & Saalfrank, P. (2011) · ChemPhysChem · doi:10.1002/cphc.201100179 · Cited by 66
Classical Simulation of Quantum Energy Flow in Biomolecules
Stock, G. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.118301 · Cited by 66
Detailed Study of DNA Hairpin Dynamics Using Single-Molecule Fluorescence Assisted by DNA Origami
Tsukanov, R., Tomov, T. E., Masoud, R., Drory, H., Plavner, N., Liber, M., & Nir, E. (2013) · The Journal of Physical Chemistry B · doi:10.1021/jp4059214 · Cited by 66
How EF-Tu can contribute to efficient proofreading of aa-tRNA by the ribosome
Noel, J. K., & Whitford, P. C. (2016) · Nature Communications · doi:10.1038/ncomms13314 · Cited by 65
Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism
Ritort, F. (2004) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2004/10/p10016 · Cited by 66
Resonant Activation in a Nonadiabatically Driven Optical Lattice
Gommers, R., Douglas, P., Bergamini, S., Goonasekera, M., Jones, P. H., & Renzoni, F. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.143001 · Cited by 66
Maximizing power and velocity of an information engine
Saha, T. K., Lucero, J. N. E., Ehrich, J., Sivak, D. A., & Bechhoefer, J. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2023356118 · Cited by 65
Aharonov–Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap
Noguchi, A., Shikano, Y., Toyoda, K., & Urabe, S. (2014) · Nature Communications · doi:10.1038/ncomms4868 · Cited by 68
Zhmurov, A. A., Dima, R. I., Kholodov, Y. A., & Barsegov, V. A. (2010) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.22824 · Cited by 65
The computation of electron transfer rates: The nonadiabatic instanton solution
Cao, J., Minichino, C., & Voth, G. A. (1995) · The Journal of Chemical Physics · doi:10.1063/1.469762 · Cited by 65
Interacting Ions in Biophysics: Real is not Ideal
Eisenberg, B. (2013) · Biophysical Journal · doi:10.1016/j.bpj.2013.03.049 · Cited by 64
Beck, D. A. C., White, G. W. N., & Daggett, V. (2006) · Journal of Structural Biology · doi:10.1016/j.jsb.2006.10.002 · Cited by 65
Some fundamental aspects of Lévy flights
Metzler, R., Chechkin, A. V., Gonchar, V. Y., & Klafter, J. (2007) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2007.01.055 · Cited by 65
Single-Molecule Recognition of Biomolecular Interaction via Kelvin Probe Force Microscopy
Park, J., Yang, J., Lee, G., Lee, C. Y., Na, S., Lee, S. W., Haam, S., Huh, Y., Yoon, D. S., Eom, K., et al. (2011) · ACS Nano · doi:10.1021/nn201540c · Cited by 65
Heterogeneous Activation, Local Structure, and Softness in Supercooled Colloidal Liquids
Ma, X., Davidson, Z. S., Still, T., Ivancic, R., Schoenholz, S. S., Liu, A. J., & Yodh, A. G. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.028001 · Cited by 65
Stochastic Resonance in an Electronic FitzHugh‐Nagumo Modela
Moss, F., Douglass, J. K., Wilkens, L. A., PIERSON, D., & Pantazelou, E. (1993) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1993.tb24679.x · Cited by 65
Tunneling dynamics in dissipative curve-crossing problems
Makarov, D. E., & Makri, N. (1993) · Physical Review A · doi:10.1103/physreva.48.3626 · Cited by 65
Sension, R. J., Harris, D. A., & Cole, A. G. (2005) · The Journal of Physical Chemistry B · doi:10.1021/jp053202w · Cited by 65
Dynamics of a two-level system with Ohmic dissipation in a time-dependent field
Dakhnovskii, Y. I. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.49.4649 · Cited by 65
Free Energy Calculations: An Efficient Adaptive Biasing Potential Method
Dickson, B. M., Legoll, F., Tony Lelièvre, A., Stoltz, G., & Fleurat‐Lessard, P. (2010) · The Journal of Physical Chemistry B · doi:10.1021/jp100926h · Cited by 64
Revisiting Bistability in the Lysis/Lysogeny Circuit of Bacteriophage Lambda
Bednarz, M., Halliday, J. A., Herman, C., & Golding, I. (2014) · PLoS ONE · doi:10.1371/journal.pone.0100876 · Cited by 61
Papazyan, A., & Maroncelli, M. (1995) · The Journal of Chemical Physics · doi:10.1063/1.468667 · Cited by 64
Decision Making in Living Cells: Lessons from a Simple System
Golding, I. (2011) · Annual Review of Biophysics · doi:10.1146/annurev-biophys-042910-155227 · Cited by 62
Excitation-Induced Stability and Phase Transition: A Review
Ibrahim, R. A. (2006) · Journal of Vibration and Control · doi:10.1177/1077546306069912 · Cited by 64
Hot-electron femtochemistry at surfaces: on the role of multiple electron processes in desorption
Gadzuk, J. W. (2000) · Chemical Physics · doi:10.1016/s0301-0104(99)00299-2 · Cited by 64
The escape problem for mortal walkers
Grebenkov, D. S., & Rupprecht, J.-F. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4976522 · Cited by 64
Grebenkov, D. S., Metzler, R., & Oshanin, G. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abb1de · Cited by 64
Cherepanov, D. A., Krishtalik, L. I., & Mulkidjanian, A. Y. (2001) · Biophysical Journal · doi:10.1016/s0006-3495(01)76084-5 · Cited by 64
Metadata
- 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
- 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
- green
- www.dora.lib4ri.ch
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
