Some properties of the entropy in the natural time.

We show that the entropy S , defined as S identical with chi ln chi - chi ln chi [Phys. Rev. E 68, 031106 (2003)] where chi stands for the natural time [Phys. Rev. E 66, 011902 (2002)], exhibits positivity and concavity as well as stability or experimental robustness. Furthermore, the distinction between the seismic electric signal activities and "artificial" noises, based on the classification of their S values, is lost when studying the time-reversed signals. This reveals the profound importance of considering the (true) time arrow.