  We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional
Kullback-Leibler entropies, induced by time-evolution of continuous probability
distributions. The question of predominantly purpose-dependent entropy
definition for non-equilibrium model systems is addressed. The conditional
Kullback-Leibler entropy is often believed to properly capture physical
features of an asymptotic approach towards equilibrium. We give arguments in
favor of the usefulness of the standard Gibbs-type entropy and indicate that
its dynamics gives an insight into physically relevant, but generally ignored
in the literature, non-equilibrium phenomena. The role of physical units in the
Gibbs-Shannon entropy definition is iscussed.
