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We report a similarity of fluctuations in equilibrium critical phenomena and non-equilibrium systems, which is based on the concept of natural time. The world-wide seismicity as well as that of San Andreas fault system and Japan are analyzed. An order parameter is chosen and its fluctuations relative to the standard deviation of the distribution are studied. We find that the scaled distributions fall on the same curve, which interestingly exhibits, over four orders of magnitude, features similar to those in several equilibrium critical phenomena ( e.g., 2D Ising model) as well as in non-equilibrium systems (e.g., 3D turbulent flow).

Three types of electric signals were analyzed: Ion current fluctuations in membrane channels (ICFMC), Seismic electric signals activities (SES), and "artificial" noises (AN). The wavelet transform, when applied to the conventional time domain, does not allow a classification of these signals, but does so in the "natural" time domain. A classification also becomes possible, if we study -(q) versus q, where chi stands for the "natural" time. For q values approximately between 1 and 2 the signals are classified and ICFMC lies between the other two types. For q=1, the "entropy" S identical with -ln of ICFMC almost equals that of a "uniform" distribution, while the AN and SES have larger and smaller S values, respectively. The recent [P. Varotsos, N. Sarlis, and E. Skordas, Phys. Rev. E 67, 021109 (2003)] finding that, in short time scales, both SES and AN (which are shown to be non-Markovian) result in comparable detrended fluctuation analysis exponents alpha in (1.0,1.5) is revisited. Even a Markovian dichotomous time series, in short time scales, leads to similar alpha exponents.

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.

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