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Volume 195, 2016
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Jump Markov models and transition state theory: the quasi-stationary distribution approach

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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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Publication details

The article was received on 06 May 2016, accepted on 07 Jun 2016 and first published on 08 Jun 2016

Article type: Paper
DOI: 10.1039/C6FD00120C
Citation: Faraday Discuss., 2016,195, 469-495
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    Jump Markov models and transition state theory: the quasi-stationary distribution approach

    G. Di Gesù, T. Lelièvre, D. Le Peutrec and B. Nectoux, Faraday Discuss., 2016, 195, 469
    DOI: 10.1039/C6FD00120C

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