In unit-birth continuous-time Markov chains with linear degradation, explicit hypotheses allow rigorous proof of a global noise tradeoff via stationary information flow, and signed monotonicity yields the termwise bound that every Fano factor is at least 1.
McAdams and Adam Arkin
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Noise Tradeoffs, Stationary Information Flow, and Structural Balance in Unit-Birth Networks
In unit-birth continuous-time Markov chains with linear degradation, explicit hypotheses allow rigorous proof of a global noise tradeoff via stationary information flow, and signed monotonicity yields the termwise bound that every Fano factor is at least 1.