Accuracy of MSD-based transport coefficient estimates at finite observation times

Ascertain whether mean-squared-displacement-based estimates of the transport coefficient D(T) are accurate when transport measurements are conducted at finite lag times, given that MSD-based transport coefficients are defined in the limit of infinite time.

Background

The authors observe strong short-time, nanoscale correlations in lipid motion that differ from bulk long-time behavior. They caution that ensemble-averaged MSD, which is defined in the long-time limit, may hide local transport processes.

This raises the methodological question of whether MSD-based D(T) estimates remain accurate when applied to finite-time nanoscale measurements.

References

Because MSD based measurements of transport coefficients are defined in the $t\rightarrow \infty$ limit, it is unclear whether MSD-based measurement of $D(T)$ is accurate or not.

— Self-diffusion is temperature independent on active membranes  (2404.10581 - Varma et al., 2024) in Results — Local diffusivity in equilibrium is T-dependent

Direct calculations from ionic MSDs are generally consistent with the force and velocity routes at $d<d^*$, but lead to a consistently higher $D_\text{MSD}^\text{MD}$ at $d>d*$ (Tables \ref{tab2} and S10). The reason for this deviation is unclear to us.

— Asymmetric Ions in Solution are Similar to Active Brownian Particles  (2608.27245 - Sarhangi et al., 27 Aug 2026) in Results section, paragraph immediately following Eq. (9)