Diffusion

The diffusion coefficient, is given by

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle D={\frac {1}{3}}\int _{0}^{\infty }\langle v_{i}(t)\cdot v_{i}(0)\rangle ~dt}

where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle v_{i}(t)} is the center of mass velovity of molecule Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle i} .

Einstein relation

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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)