Universal Correlations in Local Measurements Directly Probe Effective Diffusivity

TL;DR

This paper derives universal asymptotic forms linking local measurement autocorrelations to effective diffusivity, enabling direct microscale diffusivity measurement in various systems, validated by simulations.

Contribution

It introduces universal asymptotic formulas that connect local measurements directly to effective diffusivity, applicable at and far from equilibrium.

Findings

Universal asymptotic forms derived for autocorrelation and uncertainty.

Formulas validated across multiple models and systems.

Enables direct measurement of diffusivity using existing techniques.

Abstract

Measuring transport coefficients at the microscale remains challenging, often relying on indirect methods that require modeling and calibration. This Letter 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 are thereby elevated to asymptotically direct probes. They become capable of measuring the effective diffusivity of active and other microscopically nondiffusive systems. Simulations across several models confirm the broad applicability of these predictions.