The process of isotropic diffusion characterized by a time-dependent probability density \( P(\mathbf{x},t) \) obeys (as an approximation) the so-called Fokker-Planck equation

$$ \frac{\partial P}{\partial t} = \sum_i D\frac{\partial }{\partial \mathbf{x_i}}\left(\frac{\partial }{\partial \mathbf{x_i}} -\mathbf{F_i}\right)P(\mathbf{x},t), $$

where \( \mathbf{F_i} \) is the \( i^{th} \) component of the drift term (drift velocity) caused by an external potential, and \( D \) is the diffusion coefficient. The convergence to a stationary probability density can be obtained by setting the left hand side to zero. The resulting equation will be satisfied if and only if all the terms of the sum are equal zero,

$$ \frac{\partial^2 P}{\partial {\mathbf{x_i}^2}} = P\frac{\partial}{\partial {\mathbf{x_i}}}\mathbf{F_i} + \mathbf{F_i}\frac{\partial}{\partial {\mathbf{x_i}}}P. $$