Time-interval constraints in the quantum Zeno effect: Entropic signatures and coherence-to-decoherence transitions

The quantum Zeno effect relies on a limiting process involving the number of measurements on a system. When successive measurement intervals are subject to algebraic constraints in pairs, the effect manifests only if the constraint function decays sufficiently rapidly. A suitable functional is constructed and extremized, providing insight into the underlying procedure. The von Neumann entropy effectively identifies the coherence-to-decoherence (freeze-unfreeze) transition, with a control parameter governing this transition. Furthermore, a formal scaling law for ℏ reinforces the existence of the transition.