Universal correlations in local measurements directly probe effective diffusivity

Measuring transport coefficients at the microscale remains challenging, often relying on indirect methods that require modeling and calibration. This article derives universal asymptotic forms for the autocorrelation and relative uncertainty of local probe measurements in dilute diffusive systems. Valid both at and far from equilibrium, these forms directly connect microscopic measurements to the effective diffusivity. Indirect methods such as dynamic light scattering and fluorescence correlation spectroscopy can therefore serve as asymptotically direct probes applicable to active and other microscopically nondiffusive systems. Simulations across several models and observables confirm the broad applicability of these predictions to a variety of probes.