We show that the entropy $S$, defined as $S\equiv ⟨\chi \ln \chi ⟩-⟨\chi ⟩\ln ⟨\chi ⟩$ [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.

• Received 18 November 2004

DOI:https://doi.org/10.1103/PhysRevE.71.032102