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When particles/molecules diffuse in systems that contain obstacles, thesteady-state regime (during which the mean-square displacement scales linearlywith time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. Itis common to characterize this transient regime using the concept of anomalous(sub)diffusion with the scaling law $\left< r^2 \right> \sim t^\alpha$, wherethe corresponding exponent $\alpha<1$. We propose a new method to estimate thecritical time $t^*$ that marks the transition between these two regimes. Themethod uses short-time data from the transient regime to estimate $t^*$, whichcan then be used to estimate the steady-state diffusion coefficient $D$. Inother words, we propose a procedure that makes it possible to estimate thesteady state diffusion coefficient without reaching the steady-state. We testthe procedure with various two-dimensional lattice systems.

Estimating the Steady State Diffusion Coefficient Using Data from the Transient Anomalous Regime