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Stationary Markov jump processes in terms of average transition times: setup and some inequalities of kinetic and thermodynamic kind

The parametrization of continuous-time stationary Markov jump processes is worked out in terms of average times at which the site-to-site transitions take place again (recurrence) or occur starting from a given initial localization of the system (occurrence). The foremost result is the solution of the inverse problem of achieving the rate constants from an essential set of average occurrence/recurrence times. Then we provide the expression of the average entropy production rate at the stationary state in terms of average recurrence times only, elaborate the randomness parameter (squared coefficient of variation) which quantifies the relative precision of the timing of a given transition of interest, and derive some inequalities in which only a partial amount information about the network does enter. In particular, we get lower bounds on the randomness parameter and derive inequalities of both kinetic and thermodynamic kind.