AI Article Synopsis
- The text explores the relationship between metastable continuous state space Markov processes (like the Langevin equations) and discrete jump Markov processes.
- It emphasizes how quasi-stationary distributions can be used to effectively model exit events from metastable states, aiding in the analysis of accelerated dynamics techniques.
- Additionally, it discusses how this approach can quantify errors in parameters derived from the Eyring-Kramers formula, providing a theoretical basis for using transition state theory in kinetic modeling.
Article Abstract
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the notion of quasi-stationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the Eyring-Kramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.
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| http://dx.doi.org/10.1039/c6fd00120c | DOI Listing |
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