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 Schönes 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.

[1]  P. Varotsos,et al.  Long-range correlations in the electric signals that precede rupture. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Alejandro Ramírez-Rojas,et al.  Entropy of geoelectrical time series in the natural time domain , 2011 .

[3]  Panayiotis A. Varotsos,et al.  Natural Time Analysis: The New View of Time : Precursory Seismic Electric Signals, Earthquakes and other Complex Time Series , 2011 .

[4]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[5]  P. Varotsos,et al.  Reply to “Rebuttal to Reply by Varotsos and Lazaridou: Towards plainly successful prediction,” by Paul W. Burton , 1996 .

[6]  Andrea Donnellan,et al.  Space-time clustering and correlations of major earthquakes. , 2006, Physical review letters.

[7]  D. Applebaum.  Lévy Processes and Stochastic Calculus: Preface , 2009 .

[8]  Alejandro Ramírez-Rojas,et al.  Analysis of natural time domain entropy fluctuations of synthetic seismicity generated by a simple stick–slip system with asperities , 2015 .

[9]  Luciano Telesca,et al.  Analysis of the distribution of the order parameter of synthetic seismicity generated by a simple spring–block system with asperities , 2014 .

[10]  P. Varotsos,et al.  Detrended fluctuation analysis of the magnetic and electric field variations that precede rupture. , 2009, Chaos.

[11]  W Kent.  THE DEFINITION OF ENERGY. , 1916, Science.

[12]  Masashi Kamogawa,et al.  Natural time analysis of critical phenomena , 2011, Proceedings of the National Academy of Sciences.

[13]  M. S. Lazaridou,et al.  Fluctuations, under time reversal, of the natural time and the entropy distinguish similar looking electric signals of different dynamics , 2007, 0707.3074.

[14]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[15]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[16]  Lisa Crystal.  Energy, the Subtle Concept: The Discovery of Feynman's Blocks from Leibniz to Einstein , 2011 .

[17]  P. Varotsos,et al.  Erratum: Long-range correlations in the electric signals that precede rupture [Phys. Rev. E 66, 011902 (2002)] , 2008 .

[18]  Qinghua Huang,et al.  Forecasting the epicenter of a future major earthquake , 2015, Proceedings of the National Academy of Sciences.

[19]  Nicholas V. Sarlis,et al.  Seismic electric signals and seismicity: on a tentative interrelation between their spectral , 2002 .

[20]  E. Jaynes.  Probability theory : the logic of science , 2003 .

[21]  Antje Strauss,et al.  Energy The Subtle Concept The Discovery Of Feynmans Blocks From Leibniz To Einstein , 2016 .

[22]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[23]  Max Planck,et al.  Treatise on thermodynamics , 1928, The Mathematical Gazette.

[24]  William Klein,et al.  Probabilities for large events in driven threshold systems. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.