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 {ITALIC 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 discussed.

PACS numbers: 02.50.--r, 89.70.+c, 05.40.--a