Now let us generalize our calculation to the case when the particle transport takes place in the presence of a time-independent spatial gradient of the probability distribution caused for example by t...Now let us generalize our calculation to the case when the particle transport takes place in the presence of a time-independent spatial gradient of the probability distribution caused for example by that of the particle concentration (and hence of the chemical potential μ) while still assuming that temperature T is constant.
The first form of this relation allows a simple interpretation: the probability flow is proportional to the spatial gradient of the probability density (i.e., in application to \(N >> 1\) similar and ...The first form of this relation allows a simple interpretation: the probability flow is proportional to the spatial gradient of the probability density (i.e., in application to \(N >> 1\) similar and independent particles, just to the gradient of their concentration \(n = Nw\)), with the sign corresponding to the flow from the higher to lower concentrations.