## Einstein relation The general form of Einstein relation is $D=\mu k_{B}T$ The equation links the diffusivity $D$, mobility $\mu$, and thermodynamic quantity $k_{b}$ and $T$ together. A more common form would be Stokes-Einstein equation, describing diffusion of spherical particles, given as $D=\frac{k_{B}T}{6\pi \eta r}$Here $\eta$ is the viscosity of the medium. This form literally change the mobility with a drag coefficient, $\zeta$, using $\zeta=\frac{1}{\mu}$, while [Stokes' law](https://en.wikipedia.org/wiki/Stokes%27_law) gives $\zeta=6\pi \eta r$. Notice the $r$ stated here is the hydrodynamic radius. Only when the particles are purely spherical and have only the geometry-induced effect on the diffusivity, we have the hydrodynamic radius equal to the actual particle radius. This should be remembered when using [[Dynamic light scattering|dynamic light scattering]] to the measure particle size. Einstein relation provides an early example of a a [[Fluctuation-Dissipation theorem|fluctuation-dissipation relation]].