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Correlation Functions, Mean First Passage Times and the Kemeny Constant

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number104108
Pages (from-to)1-13
JournalJournal of Chemical Physics
Issue number10
Early online date12 Mar 2020
Accepted/In press18 Feb 2020
E-pub ahead of print12 Mar 2020
Published14 Mar 2020


King's Authors


Markov processes are widely used models for investigating kinetic networks. Here, we collate and present a variety of results pertaining to kinetic network models in a unified framework. The aim is to lay out explicit links between several important quantities commonly studied in the field, including mean first passage times (MFPTs), correlation functions, and the Kemeny constant. We provide new insights into (i) a simple physical interpretation of the Kemeny constant, (ii) a relationship to infer equilibrium distributions and rate matrices from measurements of MFPTs, and (iii) a protocol to reduce the dimensionality of kinetic networks based on specific requirements that the MFPTs in the coarse-grained system should satisfy. We prove that this protocol coincides with the one proposed by Hummer and Szabo [J. Phys. Chem. B 119, 9029 (2014)], and it leads to a variational principle for the Kemeny constant. Finally, we introduce a modification of this protocol, which preserves the Kemeny constant. Our work underpinning the theoretical aspects of kinetic networks will be useful in applications including milestoning and path sampling algorithms in molecular simulations.

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