Diffusion

The diffusion coefficient, is given by

$D={\frac {1}{3}}\int _{0}^{\infty }\langle v_{i}(t)\cdot v_{i}(0)\rangle ~dt$

where $v_{i}(t)$ is the center of mass velovity of molecule $i$.

Einstein relation

$D=\lim _{t\rightarrow \infty }{\frac {1}{6}}\langle \vert \mathbf {r} _{i}(t)\cdot \mathbf {r} _{i}(0)\vert ^{2}\rangle$

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)