Non-extensive Statistical Physics Research Articles

Superstatistical view of stress-induced electric current fluctuations in rocks

The concepts of non-extensive statistical physics, which have recently been applied in the study of complex systems, have been used here to analyse stress-induced electric current data in triaxially deformed Carrara marble samples. The fluctuations of electric current appear to follow a q-Gaussian distribution, with the PDF exhibiting ‘fat tails’. The application of super-statistical techniques to these electric current fluctuations shows to good approximation that they can be described by local Gaussian processes with fluctuating variance.

Non-extensive and natural time analysis of seismicity before the Mw6.4, October 12, 2013 earthquake in the South West segment of the Hellenic Arc

Earthquakes exhibit complex correlations in space, time, and magnitude. As such, they present a unique example for a time series exhibiting complexity. To uncover hidden dynamic features of seismicity before the Mw6.4, October 12, 2013 earthquake in the South West part of the Hellenic Arc, we apply the recently introduced methods of natural time analysis along with the ideas of non-extensive statistical physics. Using non-extensive statistics, the analysis of the magnitude distribution of the 2013 seismicity in the South West part of the Hellenic Arc, struck by a strong earthquake (Mw=6.4), was performed for a time period before the main event, which was the strongest one in the South West part of the Hellenic Arc in the last 40 years. The analysis of the frequency magnitude (energy) distribution reveals that the non-extensive parameter qE varies during the last period of the earthquake preparatory phase with a sharp increase a couple of days before the occurrence of the main strong event, indicating an increase in the degree of out-of-equilibrium state before the occurrence of the Mw6.4 earthquake. In addition using the natural time analysis it is shown that foreshock seismicity approaches the critical stage, where the k1 parameter reaches the critical value of k1=0.070 few days before the occurrence of the main event.

A Nonextensive Statistical Physics Analysis of the 1995 Kobe, Japan Earthquake

This paper presents an analysis of the distribution of earthquake magnitudes for the period 1990–1998 in a broad area surrounding the epicenter of the 1995 Kobe earthquake. The frequency–magnitude distribution analysis is performed in a nonextensive statistical physics context. The nonextensive parameter q M , which is related to the frequency-magnitude distribution, reflects the existence of long-range correlations and is used as an index of the physical state of the studied area. Examination of the possible variations of q M values is performed during the period 1990–1998. A significant increase of q M occurs some months before the strong earthquake on April 9, 1994 indicating the start of a preparation phase prior to the Kobe earthquake. It should be noted that this increase coincides with the occurrence of six seismic events. Each of these events had a magnitude M = 4.1. The evolution of seismicity along with the increase of q M indicate the system’s transition away from equilibrium and its preparation for energy release. It seems that the variations of q M values reflect rather well the physical evolution towards the 1995 Kobe earthquake.

Evidence of [formula omitted]-exponential statistics in Greek seismicity

We study the seismicity (global seismic activity) that occurred in Greece between 1976 and 2009 based on the dataset reported in Makropoulos et al. (2012), using concepts of non-extensive Statistical Physics. By considering the entire and declustered datasets, for which the aftershocks have been removed, we initially investigate the frequency–magnitude distribution and find that both datasets are well approximated by a physical model derived in the framework of non-extensive Statistical Physics. We then carry out a study of the distribution of interevent times of seismic events for different magnitude thresholds and discover that the data are well approximated by a statistical distribution of the q-exponential type that allows us to compute analytically the risk function of earthquake production. Our analysis thus reveals further evidence that the underlying dynamical process of earthquake birth reflects a kind of nonlinear memory due to long-term persistence of seismic events.

Dynamics of regional brain activity in epilepsy: a cross-disciplinary study on both intracranial and scalp-recorded epileptic seizures

Objective. Recent cross-disciplinary literature suggests a dynamical analogy between earthquakes and epileptic seizures. This study extends the focus of inquiry for the applicability of models for earthquake dynamics to examine both scalp-recorded and intracranial electroencephalogram recordings related to epileptic seizures. Approach. First, we provide an updated definition of the electric event in terms of magnitude and we focus on the applicability of (i) a model for earthquake dynamics, rooted in a nonextensive Tsallis framework, (ii) the traditional Gutenberg and Richter law and (iii) an alternative method for the magnitude–frequency relation for earthquakes. Second, we apply spatiotemporal analysis in terms of nonextensive statistical physics and we further examine the behavior of the parameters included in the nonextensive formula for both types of electroencephalogram recordings under study. Main results. We confirm the previously observed power-law distribution, showing that the nonextensive formula can adequately describe the sequences of electric events included in both types of electroencephalogram recordings. We also show the intermittent behavior of the epileptic seizure cycle which is analogous to the earthquake cycles and we provide evidence of self-affinity of the regional electroencephalogram epileptic seizure activity. Significance. This study may provide a framework for the analysis and interpretation of epileptic brain activity and other biological phenomena with similar underlying dynamical mechanisms.

Incomplete <i>E-V</i> Distribution for Shannon Entropy

Within the framework of nonextensive and incomplete statistical physics, we derive theE-Vdistribution (the extent is alterable) which is based on the deformed Shannon entropy, and discuss the revision for the traditional statistical physics (BGS) with deformed parameterq>1 andq<1 respectively, taking linear filament as an example.

Nonextensive statistical mechanics and high energy physics

The use of the celebrated Boltzmann-Gibbs entropy and statistical mechanics is justified for ergodic-like systems. In contrast, complex systems typically require more powerful theories. We will provide a brief introduction to nonadditive entropies (characterized by indices like q , which, in the q → 1 limit, recovers the standard Boltzmann-Gibbs entropy) and associated nonextensive statistical mechanics. We then present somerecent applications to systems such as high-energy collisions, black holes and others. In addition to that, we clarify and illustrate the neat distinction that exists between Levy distributions and q -exponential ones, a point which occasionally causes some confusion in the literature, very particularly in the LHC literature

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Abstract. In the present work the statistical properties of the earthquake activity in a highly seismic region, the West Corinth rift (Central Greece), are being studied by means of generalized statistical physics. By using a dataset that covers the period 2001–2008, we investigate the earthquake energy distribution and the distribution of the time intervals (interevent times) between the successive events. As has been reported previously, these distributions exhibit complex statistical properties and fractality. By using detrended fluctuation analysis (DFA), a well-established method for detection of long-range correlations in non-stationary signals, it is shown that long-range correlations are also present in the earthquake activity. The existence of these properties motivates us to use non-extensive statistical physics (NESP) to investigate the statistical properties of the frequency-magnitude and the interevent time distributions, along with other well-known relations in seismology, such as the gamma distribution for interevent times. The results of the analysis indicate that the statistical properties of the earthquake activity can be successfully reproduced by means of NESP and that the earthquake activity at the West Corinth rift is correlated at all-time scales.

A Non- Extensive statistical physics approach to the characterization of the pyroclastic deposits of the Kos volcanic center.

In this paper we present a Non-Extensive Statistical Physics (NESP) approach in order to investigate the grain size distribution of pyroclastic deposits from the Kos volcanic center that cover parts of the main Kos island as well as the surrounding areas. The Kos Plateau Tuff (KPT) of 161 Ka represents the largest Quaternary volcanic explosion of eastern Mediterranean. Pyroclastic deposits are formed by the fragmentation of magma and rocks, the driving mechanism of explosive volcanic activity. Rocks fragmentation can be considered in general as a non-linear process, where long-range interactions and scaling are important. It is exactly these processes that NESP was formed for to describe. The results of the analysis indicate that NESP is an appropriate framework for the statistical physics interpretation of volcanic rock fragmentation processes phenomena.

A Non-Extensive Statistical Physics View in the Spatiotemporal Properties of the 2003 (Mw6.2) Lefkada, Ionian Island Greece, Aftershock Sequence

Investigation of the spatiotemporal properties of the 2003 Lefkada seismic sequence is performed through non-extensive statistical physics. Information on highly accurate aftershock source parameters became feasible from the recordings of a portable digital seismological network that was installed and operated in the study area, during the evolution of the seismic sequence. Thus, the spatiotemporal distribution of aftershocks onto the main and neighboring fault segments was investigated in detail, enabling the recognition of four distinctive seismicity clusters separated by less active patches. The aftershock spatiotemporal properties are studied here, using the ideas of non-extensive statistical physics (NESP). The cumulative distribution functions of the inter-event times and the inter-event distances are presented using the data set in each seismicity cluster, and the analysis results in values for the statistical thermodynamic qT and qD parameters for each cluster, where qT varies from 1.16 to 1.47 and qD from 0.42 to 0.77 for the inter-event times and distances distributions, respectively. These values confirm the complexity and non-additivity of the spatiotemporal evolution of seismicity, and the applicability of the NESP approach in investigating aftershocks sequence. The temporal pattern is discussed using the closely connected to NESP approach of superstatistics, which is based on a superposition of ordinary local equilibrium statistical mechanics. The result indicates that the temporal evolution of the Lefkada aftershock sequence in clusters A, B and C is governed by very low number of degrees of freedom, while D is a less organized seismicity structure with a much higher number of degrees of freedom.

Evidence of Nonextensive Statistical Physics behavior of the Hellenic Subduction Zone seismicity

Abstract The Hellenic Subduction Zone (HSZ) is the most seismically active region in Europe. Many destructive earthquakes have taken place along the HSZ in the past. In this study we investigate the seismicity of the HSZ based on the science of complex systems. The spatiotemporal distributions of seismicity as well as the magnitude distribution are studied using the concept of Nonextensive Statistical Physics (NESP). Defining five seismic zones and forming an earthquake dataset that covers the period 1976–2009, we apply the NESP ideas to formulate the cumulative distribution functions of the inter-event times and distances and the magnitude distribution along the HSZ. Our results indicate that the nonextensive parameter qT, which is related with the inter-event time distribution, presents almost similar values in each of the seismic zones and reflects the long term scale of the seismicity evolution in the HSZ. The qD parameter, which is related with the inter-event distance distribution, presents a significant variation along the seismic zones. This variation is related with the different degree of spatial earthquake clustering in each of the seismic zones of the HSZ. Moreover, in the framework of the fragment–asperity model, the thermostatistical parameter qM, which is related with the frequency–magnitude distribution, could be used as an additional index to inform us about the physical state of each seismic zone along the HSZ. The variations of the qM parameter are related with the energy release rate in each seismic zone. The models used, fit rather well to the observed distributions, implying the usefulness of NESP in investigating such phenomena exhibiting scale-free nature and long range memory effects.

Electrical and Acoustic Emissions in cement mortar beams subjected to mechanical loading up to fracture

The application of mechanical loading on cement-based materials generates weak electrical currents due to the formation and propagation of microfractures. This paper introduces the simultaneous recording of electrical signal emissions know as Pressure Stimulated Currents (PSCs) and Acoustic Emissions (AEs) detected in cement mortar beams of rectangular cross-section subjected to mechanical loading using the Three Point Bending tests. The rate of the applied load during the experiments was constant up to the fracture of the specimen. The characteristics of the AE and PSC were put in contrast in order to better understand the evolution of the microfracture processes up to fracture. Specifically, the recorded PSC and AE were studied in terms of their time series, cumulative energy along with AE rate and AE interevent times that may provide information about the upcoming specimen fracture. Moreover, non-extensive statistical physics modeling was attempted in terms of studying the Tsallis entropy. Specifically, the entropic index q was calculated and its dependence on the applied mechanical load was investigated.

On the non-extensivity in Mars geological faults

A non-extensive statistical physics approach is tested for the first time in a planetary scale, for the fault length distribution in Mars estimated a non-extensive q-parameter equal to 1.277 for normal faults and 1.114 for thrust ones. The latter support the conclusion that the fault systems in Mars are subadditive ones in agreement with recent observations for faults in Earth and Valles Marineris extensional province, Mars. In addition, an analysis of the global Mars fault system as a mixed one, consisted of the normal and thrust subsystems with different q-parameters is presented, leading to q = 1.22.

Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up with these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes). We show that the populations of: (i) fracto-electromagnetic events rooted in the activation of a single fault, emerging prior to a significant earthquake, (ii) the trade volume events of different shares/economic indices, prior to a collapse, and (iii) the price fluctuation (considered as the difference of maximum minus minimum price within a day) events of different shares/economic indices, prior to a collapse, follow both the traditional Gutenberg–Richter law as well as a nonextensive model for earthquake dynamics, with similar parameter values. The obtained results imply the existence of a dynamic analogy between earthquakes and economic crises, which moreover follow the dynamics of seizures, magnetic storms and solar flares.

Evidence of non-extensivity in the seismicity observed during the 2011–2012 unrest at the Santorini volcanic complex, Greece

Abstract. During the period of October 2011–January 2012, an increase of earthquake activity has been observed in the volcanic complex of Santorini Island, Greece. Herein, the magnitude distribution of earthquakes as well as the temporal distribution of seismicity are studied. The statistics of both parameters exhibit complexity that is evident in the frequency-magnitude distribution and the inter-event time distribution, respectively. Because of this, we have used the analysis framework of non-extensive statistical physics (NESP), which seems suitable for studying complex systems. The observed inter-event time distribution for the swarm-like earthquake events, as well as the energy and the inter-event earthquake energy distributions for the observed seismicity can be successfully described with NESP, indicating the inherent complexity of the Santorini volcanic seismicity along with the applicability of the NESP concept to volcanic earthquake activity, where complex correlations exist.

Evidence of non-extensive statistical physics of the lithospheric instability approaching the 2004 Sumatran–Andaman and 2011 Honshu mega-earthquakes

In the present study, we demonstrate in the frame of non-extensive statistical physics, significant deviations of the global seismic activity from a quasi-stationary regime before Sumatra–Andaman and Honshu mega-earthquakes suggesting the existence of a global scale intermediate-term non-extensive tectonic premonitory of impending mega-earthquake processes in the lithosphere.Using non-extensive statistical mechanics we describe the frequency–moment, the inter-event time and distance distributions, interpreting Sumatran's (2004) and Honshu (2011) earthquakes influence on these. At a phenomenological level, we find that global seismicity is described by non-extensive statistical mechanics (NESM) and that the seismic moment and the earthquake inter-event time distributions reflect a sub-extensive system, where long-range interactions are important. Using the cross-over formulation of NESM leads us to the conclusion that the seismic moment distribution of moderate events yields thermodynamic q-values of qM=1.6 which seem to be constant for the duration of the Sumatra and Honshu earthquake preparation, while rM (which describes the seismic moment distribution of great events) varies from 1 to 1.5 as we approach the mega events, The inter-event time and inter-event distance distributions, with qτ=1.5, and qD=0.3, respectively support the conclusion of non-extensive “spatio-temporal duality”, suggesting that global shallow moderate seismicity (with 5.5<Mw<Mc=7.5) is described in a unique way by the q-value triplet (qM,qτ,qD)=(1.6, 1.5, 0.3), independently from the influence of seismic mega events, while the preparatory process is described by the variation of rM, which has a value rM=1, consistent with an exponential roll-off years before the Sumatra event. A deviation occurred after 1993 or later when the frequency–moment distribution of the global seismic activity at shallow depths appears as a general straightening, suggesting a deviation of r-parameter from r=1 to a value r≈1.4–1.5 evidently due to the apparent rise of the rate of strong earthquakes.

Dynamical analogy between epileptic seizures and seismogenic electromagnetic emissions by means of nonextensive statistical mechanics

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and neurodynamics can be analyzed within similar mathematical frameworks. Recently, authors have shown that a dynamical analogy supported by scale-free statistics exists between seizures and earthquakes, analyzing populations of different seizures and earthquakes, respectively. The purpose of this paper is to suggest a shift in emphasis from the large to the small scale: our analyses focus on a single epileptic seizure generation and the activation of a single fault (earthquake) and not on the statistics of sequences of different seizures and earthquakes. We apply the concepts of the nonextensive statistical physics to support the suggestion that a dynamical analogy exists between the two different extreme events, seizures and earthquakes. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes and the distribution of the waiting time until the next event). The performed analysis confirms the existence of a dynamic analogy between earthquakes and seizures, which moreover follow the dynamics of magnetic storms and solar flares.

Experimental evidence of a non-extensive statistical physics behavior of electromagnetic signals emitted from rocks under stress up to fracture. Preliminary results

The application of mechanical stress on a rock sample can induce electromagnetic emissions. Such emissions can be detected experimentally and in principle could be used as precursors of the upcoming failure. Using experimental observations of stress-induced electromagnetic emissions (SIEME), we apply the concepts of non-extensive statistical physics (NESP) to the time intervals between consecutive SIEME. The application of NESP is appropriate to systems such as fracture-induced effects, where non-linearity, long-range interactions and scaling are important. We find that the SIEME energy release distribution and the inter-event time distribution reflect a sub-extensive system with thermodynamic q-values of the order of q E = 1.67 and q τ ≈ 1.7, respectively.

Emulation of simulated earthquake catalogues

In earthquake occurrence studies, the so-called q value can be considered both as one of the parameters describing the distribution of interevent times and as an index of non-extensivity. Using simulated datasets, we compare four kinds of estimators, based on principle of maximum entropy (POME), method of moments (MOM), maximum likelihood (MLE), and probability weighted moments (PWM) of the parameters (q and τ0) of the distribution of inter-events times, assumed to be a generalized Pareto distribution (GPD), as defined by Tsallis (1988) in the frame of non-extensive statistical physics. We then propose to use the unbiased version of PWM estimators to compute the q value for the distribution of inter-event times in a realistic earthquake catalogue simulated according to the epidemic type aftershock sequence (ETAS) model. Finally, we use these findings to build a statistical emulator of the q values of ETAS model. We employ treed Gaussian processes to obtain partitions of the parameter space so that the resulting model respects sharp changes in physical behaviour. The emulator is used to understand the joint effects of input parameters on the q value, exploring the relationship between ETAS model formulation and distribution of inter-event times.

A non-extensive statistical physics view to the spatiotemporal properties of the June 1995, Aigion earthquake (M6.2) aftershock sequence (West Corinth rift, Greece)

In the present study, the spatiotemporal properties of the Aigion earthquake (15 June 1995) aftershock sequence are being studied using the concept of non-extensive statistical physics (NESP). The cumulative distribution functions of the inter-event times and the inter-event distances are being estimated for the data set which is assumed to be complete and the analysis yielded the thermodynamic q parameter to be qT = 1.58 and qr = 0.53 for the two distributions, respectively. The results fit rather well to the inter-event distances and times distributions, implying the complexity of the spatiotemporal properties of seismicity and the usefulness of NESP in investigating such phenomena. The temporal structure is also being discussed using the complementary to NESP approach of superstatistics, which is based on a superposition of ordinary local equilibrium statistical mechanics. The result indicates that very low degrees of freedom describe the temporal evolution of the Aigion earthquake aftershock seismicity.