A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution

Abstract

Abstract:In the volcanic complex processes, inherent long-range interactions exist suggesting that Non-Extensive Statistical mechanics could be used to describe fundamental properties of the system. Based on the non-extensive Tsallis entropy a frequency-volume distribution function is suggested for the Easter Island-Salas y Gomez seamounts chain. Our results demonstrate the applicability of fundamental principles of Tsallis entropy to derive the cumulative distribution of seamounts volumes. The work suggests that the processes responsible for hotspot seamount formation are complex and the cumulative frequency-volume distribution of seamounts in the Easter Island/Salas y Gomez Chain (ESC) are well-described by a q-exponential function. The analysis leads to a non-extensive index q = 1.54 in agreement with that presented in other geodynamic or laboratory scale effects.

Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere

“…Also worth mentioning are selected entropic applications beyond BG in other areas of knowledge: complex networks [ 16 , 17 , 18 ]; economics [ 149 , 150 , 151 , 152 , 153 , 154 , 155 , 156 ]; geophysics (earthquakes, atmosphere) [ 157 , 158 , 159 , 160 , 161 , 162 , 163 , 164 , 165 , 166 ]; general and quantum chemistry [ 139 , 167 , 168 , 169 , 170 , 171 ]; hydrology and engineering (water engineering [ 172 ] and materials engineering [ 173 , 174 ]); power grids [ 175 ]; the environment [ 176 ]; medicine [ 177 , 178 , 179 ]; biology [ 180 , 181 ]; computational processing of medical images (microcalcifications in mammograms [ 182 ] and magnetic resonance for multiple sclerosis [ 183 ]) and time series (e.g., ECG in coronary disease [ 184 ] and EEG in epilepsy [ 185 , 186 ]); train delays [ 187 ]; citations of scientific publications and scientometrics [ 188 , 189 ]; global optimization techniques [ 190 ...…”

The use of acoustic emissions technique in the monitoring of fracturing in concrete using soundless chemical demolition agent

“…In the case of the recorded AE activity during the fracture of brittle materials (concrete and rocks), the continuous variable X corresponds to an AE parameter, such as the inter-event time or inter-event distance between two successive micro-cracks generated within the material, due to the applied mechanical stress [24,26,27]. The maximization of q-entropy under appropriate constraints generates probability distributions, the so-called q-distributions, such as q-exponential, q-Gaussian, q-Weibull distributions, etc [32][33][34]. The q-exponential distribution has been extensively used to describe the cumulative distribution functions (CDF) of seismic parameters in global and regional scale, and the AE activity in laboratory-scale fracturing experiments of rocks [24][25][26][27][28].…”

Complexity of the Yellowstone Park Volcanic Field Seismicity in Terms of Tsallis Entropy

“…The objectives of the present work are to study, in terms of Tsallis entropy, the spatial properties of magnitude–frequency distribution of seismicity in complex systems where fracturing and strong correlations exist, such as in the volcanotectonic Yellowstone system, along with the spatiotemporal properties of the swarms which occurred on the Yellowstone Lake during December–January 2008–2009 and the 2010 Madison Plateau using the ideas of Non-Extensive Statistical Physics (NESP) and Tsallis entropy [ 10 , 11 , 12 ], which is one of the entropies used within the family of generalized entropies (see [ 13 , 14 , 15 , 16 , 17 ]). Since the complexity issues related with Geophysical problems are not high-order issues, the applicability of Tsallis entropy in Earth physics has been demonstrated in a series of recent publications on seismicity [ 18 , 19 , 20 , 21 , 22 ], natural hazards [ 23 , 24 ], plate tectonics [ 25 ], geomagnetic reversals [ 26 ], volcanic systems [ 27 ], rock physics [ 28 ], applied geophysics [ 29 ], and fault-length distributions [ 30 , 31 ]. Using the seismic data provided by the University of Utah Seismological Stations (UUSS), we analyzed the inter-event time and distance distributions of the earthquakes that occurred during the two swarms, fitting the observed data with the q -exponential function that maximizes the Tsallis entropy, along with the magnitude-frequency distribution, as formulated in the frame of NESP [ 32 ].…”