### Abstract

The results of transition state theory are derived rigorously in the general context of ergodic dynamical systems defined by a vector field on a Riemannian manifold. A new perspective on how to compute the dynamical corrections to the transition state theory transition frequency is given. Hamiltonian dynamical systems are considered a special case and the so-called Marcus formula for the rate constant is re-derived.

Original language | English (US) |
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Pages (from-to) | 501-509 |

Number of pages | 9 |

Journal | Nonlinearity |

Volume | 19 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2006 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

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## Cite this

Tal, F. A., & Vanden-Eijnden, E. (2006). Transition state theory and dynamical corrections in ergodic systems.

*Nonlinearity*,*19*(2), 501-509. https://doi.org/10.1088/0951-7715/19/2/014