Entropy in the natural time domain

Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined and complexity measures based on this entropy as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena like the El Nino/La Nina Southern Oscillation.

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Analysis of natural time domain entropy fluctuations of synthetic seismicity generated by a simple stick–slip system with asperities

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2014.10.037 ◽

2015 ◽

Vol 419 ◽

pp. 23-28 ◽

Cited By ~ 8

Author(s):

C.A. Vargas ◽

E.L. Flores-Márquez ◽

A. Ramírez-Rojas ◽

L. Telesca

Keyword(s):

Slip System ◽

Time Domain ◽

Stick Slip ◽

Natural Time

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Flux avalanches inYBa2Cu3O7−xfilms and rice piles: Natural time domain analysis

Physical Review B ◽

10.1103/physrevb.73.054504 ◽

2006 ◽

Vol 73 (5) ◽

Cited By ~ 21

Author(s):

N. V. Sarlis ◽

P. A. Varotsos ◽

E. S. Skordas

Keyword(s):

Time Domain ◽

Time Domain Analysis ◽

Domain Analysis ◽

Natural Time ◽

Flux Avalanches

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Detecting Criticality by Exploring the Acoustic Activity in Terms of the “Natural-Time” Concept

Applied Sciences ◽

10.3390/app12010231 ◽

2021 ◽

Vol 12 (1) ◽

pp. 231

Author(s):

Andronikos Loukidis ◽

Dimos Triantis ◽

Ilias Stavrakas ◽

Ermioni D. Pasiou ◽

Stavros K. Kourkoulis

Keyword(s):

Power Law ◽

Time Domain ◽

Temporal Evolution ◽

Critical Stage ◽

Acoustic Activity ◽

Natural Time ◽

Self Consistent ◽

Impending Fracture

The acoustic activity developed in marble specimens under various loading schemes is explored in terms of the recently introduced F-function. The novelty of the study is that instead of describing the temporal evolution of the F-function in terms of conventional time, the Natural Time concept is employed. Although completely different geometries and loading schemes were considered, the evolution of the F-function in the Natural Time domain exhibits a self-consistent motive: its values increase progressively with fluctuations of varying intensity, however, while the fracture is approaching, a power law appears to systematically govern the response of the specimen/structure loaded. The exponent of this law, somehow corresponding to the intensity of the acoustic activity within the loaded complex, varies within broad limits. The onset of validity of the power law designates that the system has entered into its critical stage, namely that of impending fracture, providing a useful pre-failure signal.

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Entropy of geoelectrical time series in the natural time domain

Natural Hazards and Earth System Science ◽

10.5194/nhess-11-219-2011 ◽

2011 ◽

Vol 11 (1) ◽

pp. 219-225 ◽

Cited By ~ 20

Author(s):

A. Ramírez-Rojas ◽

L. Telesca ◽

F. Angulo-Brown

Keyword(s):

Time Series ◽

Time Domain ◽

Chaotic Map ◽

Low Frequency ◽

Artificial Noise ◽

Strong Earthquakes ◽

Natural Time ◽

Correlation Degree ◽

Electric Signals ◽

Simulated Time

Abstract. Seismic electric signals (SES) have been considered precursors of strong earthquakes, and, recently, their dynamics have been investigated within the Natural Time Domain (NTD) (Varotsos et al., 2004). In this paper we apply the NTD approach and the chaotic map signal analysis to two geoelectric time series recorded in a seismically very active area of Mexico, where two strong earthquakes, M=6.6 and M=7.4, occurred on 24 October 1993 and 14 September 1995, respectively. The low frequency geoelectric signals measured display periods with dichotomic behavior. Our findings point out to an increase of the correlation degree of the geoelectric signals before the occurrence of strong earthquakes; furthermore, the power spectrum and entropy in NTD are in good agreement with the results published in literature. Our results were validated by the analysis of a chaotic map simulated time series, which revealed the typical characteristics of artificial noise.

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