Diffusion vs mobility and the Einstein relation

This [former question](https://chemistry.stackexchange.com/questions/169168/how-to-estimate-the-mobility-constant-and-the-surface-energy-parameter-in-the-ca) is about the mobility constant $M>0$ in the Cahn-Hilliard equation. To determine the value of such a mobility for a simulation study, [Kim and Sanders (2020)](https://www.sciencedirect.com/science/article/abs/pii/S0022309319304624)
use the formula
$$
M = \frac{D \cdot N\_A}{\partial^2 G / \partial c^2},\qquad \text{(\*)}
$$
where $D$ is the diffusion coefficient, $N\_A$ is the number of particles per unit area, $G$ is the molar Gibbs free energy and $c$ is the molar fraction.


**Question:** Where does the formula (\*) come from? Does this formula have something do to with the [Einstein relation](https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory))?


