The Spectral Cost of Detecting Nonequilibrium at Finite Temporal Resolution

Abstract

A detector that cannot take two snapshots closer than a time $τ_0$ still identifies a fully observed finite Markov generator exactly, provided its gaps are randomized by two clocks. Identification is not detection. For a normal nonequilibrium network, the number of snapshots needed to reject every hidden equilibrium explanation grows as $e^{2γ_{\mathrm{irr}}τ_0}$, where $γ_{\mathrm{irr}}$ is the slowest damping of rotating modes. No adaptive schedule beats this rate, and a test on one dependent trajectory attains it.