The Smoluchowski-Chapman-Kolmogorov functional equation is applied to the electric signals that precede rupture. The results suggest a non-Markovian character of the analyzed data. The rescaled range Hurst and detrended fluctuation analyses, as well as that related with the “mean distance a walker spanned,” lead to power-law exponents, which are consistent with the existence of long-range correlations. A “universality” in the power spectrum characteristics of these signals emerges, if an analysis is made (not in the conventional time frame, but) in the “natural” time domain. Within this frame, it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture. The latter exhibit a behavior compatible with that expected from a model based on the random field Ising Hamiltonian at the critical point.

The correlations within the time series of the seismic electric signal (SES) activities have been studied in a previous paper [P. Varotsos, N. Sarlis, and E. Skordas, Phys. Rev. E 66, 011902 (2002)]. Here, we analyze the time series of successive high- and low-level states’ durations. The existence of correlation between the states is investigated by means of Hurst and detrended fluctuation analysis (DFA). The multifractal DFA (MF-DFA) is also employed. The results point to a stronger correlation, and hence longer memory, in the series of the high-level states. Furthermore, an analysis in the “natural” time domain reveals that certain power spectrum characteristics seem to distinguish SES activities from “artificial” (man-made) electric noises. More precisely, for natural frequencies $0<\mathrm{}\phi <0.5,$ the curves of the SES activities and artificial noises lie above and below, respectively, that of the “uniform” distribution (UD). A classification of these two types of electric signals (SES activities, artificial noises), cannot be achieved on the basis of the values of the power-law exponents alone, if the Hurst analysis, DFA, and MF-DFA are applied to the original time series. The latter two methods, however, seem to allow a distinction between the SES activities and artificial noises when treating them (not in conventional the time frame, but) in the natural time domain. To further test the techniques, a time series produced by another system was examined. We chose a signal of ion current fluctuations in membrane channels (ICFMCs). The following conclusions, among others, have been obtained: First, the power spectrum analysis in the natural time domain shows that the ICFMC curve almost coincides (in the range $0<\mathrm{}\phi <0.5)$ with that of the UD, and hence ICFMC lies just in the boundary between the SES activities and artificial noises. Second, MF-DFA indicates monofractality for the ICFMCs with a generalized Hurst exponent $h=0.84\mathrm{}\pm 0.03$ in the range 7–70 ms.