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Markov processes are widely used models for investigating kinetic networks.Here we collate and present a variety of results pertaining to kinetic networkmodels, in a unified framework. The aim is to lay out explicit links betweenseveral important quantities commonly studied in the field, including meanfirst passage times (MFPTs), correlation functions and the Kemeny constant, andhighlight some of the subtleties which are often overlooked in the literature,while providing new insights. Results include (i) a simple physicalinterpretation of the Kemeny constant, (ii) a recipe to infer equilibriumdistributions and rate matrices from measurements of MFPTs, potentially usefulin applications, including milestoning in molecular dynamics, and (iii) aprotocol to reduce the dimensionality of kinetic networks, based on specificrequirements that the MFPTs in the coarse-grained system should satisfy. It isproven that this protocol coincides with the one proposed by Hummer and Szaboin [1] and it leads to a variational principle for the Kemeny constant. We hopethat this study will serve as a useful reference for readers interested intheoretical aspects of kinetic networks, some of which underpin usefulapplications, including milestoning and coarse-graining.

Correlation Functions, Mean First Passage Times and the Kemeny Constant