Metastability, conformation dynamics, and transition pathways in complex systems

  • E. Weinan
  • Eric Vanden-Eijnden
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 39)


We present a systematic introduction to the basic concepts and techniques for determining transition pathways and transition rates in systems with multiple metastable states. After discussing the classical transition state theory and its limitations, we derive a new set of equations for the optimal dividing surfaces. We then discuss transition path sampling, which is the most general technique currently available for determining transition regions and rates. This is followed by a discussion on minimal energy path for systems with smooth energy landscapes. For systems with rough energy landscapes, our presentation is centered around the notion of reaction coordinates. We discuss the two related notions of free energies associated with a reaction coordinate, and show that at least in the high friction limit, there does exist an optimal reaction coordinate that gives asymptotically the correct prediction for the transition rates. Variational principles associated with the optimal reaction coordinates are exploited under the assumption that the transition paths are restricted to tubes, and this provides a theoretical justification for the finite temperature string method. Blue moon sampling techniques, metadynamics and a new form of accelerated dynamics are also discussed.


Transition State Theory Transition Path Transition Pathway Transition Path Sampling Conformation Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • E. Weinan
    • 1
  • Eric Vanden-Eijnden
    • 2
  1. 1.Department of Mathematics and PACMPrinceton UniversityPrincetonUSA
  2. 2.Courant InstituteNew York UniversityNew YorkUSA

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