The Detector Before the System - Spurious Rate Anomalies in Discretely Sampled Threshold Detection
Year: 2026
Type: preprint
Abstract: A threshold applied to a noisy, continuously fluctuating record does not define an event rate at all until a second, rearm threshold is imposed. This paper gives the closed form that follows and turns it into a pre-computable test quantity for any reported rate anomaly from a threshold-based measurement. Many experiments count events by applying a threshold to a continuously fluctuating, noisy record: telegraph noise in a resistance trace, an idealised single-channel current, a filtered voltage trace. Such a detector has no event rate that is a property of the process rather than of the acquisition chain until a second threshold is imposed. With a rearm threshold — a Schmitt trigger — the rate is well defined, and the mean inter-event interval has a closed form in which the two first-passage contributions collapse onto the separation of the thresholds, their absolute positions cancelling: ⟨T⟩ = π(Δφ + 2s)/(2γ), with s = 0.5826·√(2γΔt), the continuity correction for discretely monitored barriers. From this follows the practical result: a detector whose time resolution does not scale with the observed process reports a rate change of predictable size where nothing but the sampling grid has acted. In laboratory units the relative bias is ε ≈ 1.1652 σ_step/ΔV, the ratio of the per-sample RMS step of the monitored signal to the trigger-to-rearm separation — both read directly off the record. Holding the sampling interval fixed across a factor of eight in process speed shifts the apparent rate by (7.0 ± 0.5) % and separates the normalised interval distributions at two-sample Kolmogorov–Smirnov p < 10⁻²³: highly significant and entirely instrumental. Two further consequences carry the same √Δt constant: reported two-state occupancies are biased toward 1/2, and recorded maxima rise with the sampling rate. The application worked through is the readout of superparamagnetic tunnel junctions for probabilistic computing, where the signature is already visible in published device data. The contribution is a test quantity, not new physics; it belongs upstream of the environmental controls such analyses usually invoke.
Author: Zander, Fabio
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203580013