  We start with a global Maxwellian $M_{k}$, which is a stationary solution,
with the constant total density ($\rho(t)\equiv \wt \rho$), of the
Fokker-Planck equation. The notion of distance between the function $M_{k}$ and
an arbitrary solution $f$ (with the same total density $\wt \rho$ at the fixed
moment $t$) of the Fokker-Planck equation is introduced. In this way, we
essentially generalize the important Kullback-Leibler distance, which was
studied before. Using this generalization, we show local stability of the
global Maxwellians in the spatially inhomogeneous case. We compare also the
energy and entropy in the classical and quantum cases.
