In the above-mentioned paper by Dunkel and Trigger [Phys. Rev. A 71, 052102 (2005)] a hypothesis has been pursued that the loss of information associated with the quantum evolution of pure states, quantified in terms of an increase in the time of so-called Leipnik's joint entropy, could be a rather general property shared by many quantum systems. This behavior has been confirmed for the unconfined model systems and properly tuned initial data (maximally classical states). We provide two particular examples which indicate a complexity of the quantum evolution. In the presence of a confining (harmonic) potential Leipnik's entropy there may be nonincreasing for maximally classical initial data. Another choice of initial data implies periodicity in the time of the Leipnik entropy.