On the motivation and foundation of Natural Time Analysis: Useful remarks

Since its introduction in 2001, natural time analysis has been applied to diverse fields with remarkable results. Its validity has not been doubted by any publication to date. Here, we indicate that frequently asked questions on the motivation and the foundation of natural time analysis are directly answered if one takes into account the following two key points that we have considered as widely accepted when natural time analysis was proposed: First, the aspects on the energy of a system forwarded by Max Planck in his Treatise on Thermodynamics. Second, the theorem on the characteristic functions of probability distributions which Gauss called Ein Sch\"ones Theorem der Wahrscheinlichkeitsrechnung (beautiful theorem of probability calculus). The case of the time series of earthquakes and of the precursory Seismic Electric Signals are discussed as typical examples.Comment: 17 pages including 1 figure. Accepted for publication in Acta Geophysica on May 1, 201

Geoelectric field and seismicity changes preceding the 2018 Mw6.8 earthquake and the subsequent activity in Greece

A strong earthquake of magnitude Mw6.8 struck Western Greece on 25 October 2018 with epicenter at 37.515N 20.564E. It was preceded by an anomalous geolectric signal that was recorded on 2 October 2018 at a measuring station 70km away from the epicenter. Upon analyzing this signal in natural time, we find that it conforms to the conditions suggested (e.g., Entropy 19 (2017) 177) for its identification as precursory Seismic Electric Signal (SES) activity. Notably, the observed lead time of 23 days lies within the range of values that has been very recently identified (Entropy 20 (2018) 561) as being statistically significant for the precursory variations of the electric field of the Earth. Moreover, the analysis in natural time of the seismicity subsequent to the SES activity in the area candidate to suffer this strong earthquake reveals that the criticality conditions were obeyed early in the morning of 18 October 2018, i.e., almost a week before the strong earthquake occurrence, in agreement with earlier findings. Furthermore, upon employing the recent method of nowcasting earthquakes, which is based on natural time, we find an earthquake potential score around 80% just before the occurrence of this Mw6.8 earthquake. In the present version of this manuscript, we also report the recording of additional SES activities after the occurrence of the latter earthquake and update the results until 16 April 2019.Comment: 10 pages including 12 figures. The major part of this paper appeared in Entropy 20 (2018) 882 by the first two author

Bulk moduli of PbSx_{x}Se1−x_{1-x}, PbSx_{x}Te1−x_{1-x}, and PbSex_{x}Te1−x_{1-x} from the combination of the cBΩcB\Omega model with the modified Born theory compared to generalized gradient approximation

The bulk moduli of PbS$_{x}$Se$_{1-x}$, PbS$_{x}$Te$_{1-x}$, and PbSe$_{x}$Te$_{1-x}$ have been recently determined [E. Skordas, Materials Science in Semiconductor Processing 43 (2016) 65-68] by employing a thermodynamical model, the so called $cB\Omega$ model, which has been found to give successful results in several applications of defects in solids. Here, we suggest an alternative procedure for this determination which combines the $cB\Omega$ model with the modified Born theory. The results are in satisfactory agreement with those deduced independently by the generalized gradient approximation approach.Comment: 11 pages, 1 figur