The Spectral Cost of Detecting Nonequilibrium at Finite Temporal Resolution

A detector that cannot take two snapshots closer than a time ${\tau }_0$ 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 $e^{2{\gamma }_{\mathrm{i}\mathrm{r}\mathrm{r}}{\tau }_0}$, where ${\gamma }_{\mathrm{i}\mathrm{r}\mathrm{r}}$ is the slowest damping of rotating modes. No adaptive schedule beats this rate, and a test on one dependent trajectory attains it.