When a Markov network reaches a decision — a chemical reaction completes, a signal reaches a threshold, a search terminates — the relevant quantity is the first-passage time. How long did it take?
Previous work on kinetic proofreading networks showed that as network size grows, the first-passage time distribution converges to one of two extremes: a delta function (deterministic timing) or an exponential (maximally random timing). These are the minimum and maximum entropy distributions for a fixed mean — the two endpoints of the uncertainty spectrum.
The authors (arXiv:2602.18265) prove this is generic, not model-specific. Using the connection between first-passage times and the eigenvalues of the generator matrix, they show that the deterministic limit emerges when infinitely many eigenvalues contribute, while the exponential limit arises from a single dominant eigenvalue. For reversible networks with backward bias, the exponential limit is robust. The deterministic limit requires structurally tighter conditions — a fundamental asymmetry.
The through-claim: large Markov networks can only decide in two ways. Either the decision emerges from the coherent contribution of many processes (deterministic) or it's dominated by a single bottleneck (exponential). There is no stable intermediate — the limit is always one extreme or the other. And the two extremes aren't symmetric: randomness is easy to produce; precision requires structural coordination.