Diffusion

The diffusion coefficient, is given by

$D=\frac{1}{3}\underset{0}{\overset{\mathrm{\infty }}{\int }}⟨v_i(t)\cdot v_i(0)⟩dt$

where $v_i(t)$ is the center of mass velovity of molecule $i$.

Einstein relation

$D=\underset{t\to \mathrm{\infty }}{lim}\frac{1}{6}⟨|{\mathbf{r}}_i(t)\cdot {\mathbf{r}}_i(0){|}^2⟩$

References

1. G. L. Aranovich and M. D. Donohue "Limitations and generalizations of the classical phenomenological model for diffusion in fluids", Molecular Physics 105 1085-1093 (2007)