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Simple examples of continuous-time Markov-chain models for reactions

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Abstract

We describe here several uses of simple continuous-time Markov chains in the study of reaction networks. We describe in particular how the use of a Markov chain can simplify and clarify the analysis of an isomerization network, and how it can identify illegal loops in such a network, that is, cases in which detailed balance is not satisfied. We then describe how ‘additive reversiblization’ can be used to impose (Markov-chain) detailed balance on a network, and provide an example of its use to ‘repair’ an illegal loop identified in the chemical literature.

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Notes

  1. Or as the author Malcolm Gladwell [9] might call them, igon values.

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Acknowledgements

Dr Alex Mitrophanov is thanked for re-awakening the author’s interest in Markov chains in continuous time. The editor and an anonymous reviewer are thanked for their helpful suggestions, as are Prof. Linda Haines and Dr Etienne Pienaar.

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  1. University of Cape Town, Rondebosch, 7701, South Africa

    Iain L. MacDonald

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Correspondence to Iain L. MacDonald.

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MacDonald, I.L. Simple examples of continuous-time Markov-chain models for reactions. Reac Kinet Mech Cat 136, 1–11 (2023). https://doi.org/10.1007/s11144-023-02348-5

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