Search Results (74)

On 2 December 2020, an earthquake with a magnitude of M_w 4.5 occurred near the city of Thiva (Greece). The aftershock sequence, triggered by ruptures on or near the Kallithea fault, continued until January 2021. Seven months later, new seismic activity began a few kilometers west of the initial events, with the swarm displaying a general trend of spatiotemporal migration toward the east–southeast until the middle of 2022. In order to understand the physical and statistical pattern of the swarm, the seismicity was relocated using HypoDD, and the magnitude of completeness was determined using the frequency–magnitude distribution. In order to define the existence of spatiotemporal seismicity clusters in an objective way, the DBSCAN clustering algorithm was applied to the 2020–2022 Thiva earthquake sequence. The extracted clusters permit the analysis of the spatiotemporal scaling properties of the main clusters using the Non-Extensive Statistical Physics (NESP) approach, providing detailed insights into the nature of the long-term correlation of the seismic swarm. The statistical pattern observed aligns with a Q-exponential distribution, with q_D values ranging from 0.7 to 0.8 and q_T values from 1.44 to 1.50. Furthermore, the frequency–magnitude distributions were analyzed using the fragment–asperity model proposed within the NESP framework, providing the non-additive entropic parameter (q_M). The results suggest that the statistical characteristics of earthquake clusters can be effectively interpreted using NESP, highlighting the complexity and non-additive nature of the spatiotemporal evolution of seismicity. In addition, the analysis of the properties of the seismicity clusters extracted using the DBSCAN algorithm permits the suggestion of possible physical mechanisms that drive the evolution of the two main and larger clusters. For the cluster that activated first and is located in the west–northwest part, an afterslip mechanism activated after the 2 September 2021, M 4.0 events seems to predominately control its evolution, while for the second activated cluster located in the east–southeast part, a normal diffusion mechanism is proposed to describe its migration pattern. Concluding, we can state that in the present work the application of the DBSCAN algorithm to recognize the existence of any possible spatiotemporal clustering of seismicity could be helping to provide detailed insight into the statistical and physical patterns in earthquake swarms. Full article

The thermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields can be described by kappa distributions. The kappa distribution provides a replacement for the Maxwell–Boltzmann distribution, which can be considered as a generalization for describing systems characterized by local correlations among their particles, as found in space and astrophysical plasmas. This paper presents all special cases of kappa distributions as members of a general pathway family of densities introduced by Mathai. The aim of the present paper is to bring to attention the application of various forms of the kappa distribution, its various special cases and its generalizations, which, in scalar-variable and multivariate situations, belong to a general family of distributions known as Mathai’s pathway models, comprising three different families of functions, namely the generalized type-1 beta, type-2 beta and gamma families. Through one parameter, known as the pathway parameter, one will be able to reach all the three families of functions and the stages of transitioning from one family to another. After pointing out the connection of multivariate (vector-variate) kappa distributions to the multivariate pathway model, the multivariate kappa distribution is extended to the real matrix-variate case by working out the various forms and by evaluating the normalizing constants of the various forms of the matrix-variate case explicitly. It is also pointed out that the pathway models are available for the scalar, vector and rectangular matrix-variate cases in the real domain as well as in the complex domain. Full article

This study employs Monte Carlo (MC) models and thermal-statistical analysis to investigate the production mechanisms of strange ($K_S^0$, $\mathrm{\Lambda }$) and multi-strange ($\mathrm{\Xi }$, $\mathrm{\Omega }$) hadrons in high-multiplicity proton–proton collisions. Through systematic comparisons with experimental data, we evaluate the predictive power of EPOS, PYTHIA8, QGSJETII04, and Sibyll2.3d. EPOS, with its hydrodynamic evolution, successfully reproduces low-$p_T$$K_S^0$ and $\mathrm{\Lambda }$ yields in high-multiplicity classes (MC1–MC3), mirroring quark-gluon plasma (QGP) thermalization effects. PYTHIA8’s rope hadronization partially mitigates mid-$p_T$ multi-strange baryon suppression but underestimates $\mathrm{\Xi }$ and $\mathrm{\Omega }$ yields due to the absence of explicit medium dynamics. QGSJETII04, tailored for cosmic-ray showers, overpredicts soft $K_S^0$ yields from excessive soft Pomeron contributions and lacks multi-strange hadron predictions due to enforced decays. Sibyll2.3d’s forward-phase bias limits its accuracy at midrapidity. No model fully captures $\mathrm{\Xi }$ and $\mathrm{\Omega }$ production, though EPOS remains the closest. Complementary Tsallis distribution analysis reveals a distinct mass-dependent hierarchy in the extracted effective temperature ($T_{\mathrm{eff}}$) and non-extensivity parameter (q). As multiplicity decreases, $T_{\mathrm{eff}}$ rises while q declines—a trend amplified for heavier particles. This suggests faster equilibration of heavier particles compared to lighter species. The interplay of these findings underscores the necessity of incorporating QGP-like medium effects and refined strangeness enhancement mechanisms in MC models to describe small-system collectivity. Full article

The observed scaling properties in the three aftershock sequences of the recent strong earthquakes of magnitudes M_w 6.1, M_w 6.4 and M_w 6.7, which occurred in the Ionian island region on the 26 January 2014 (onshore Cephalonia Island), 17 November 2015 (Lefkada Island) and 25 October 2018 (offshore Zakynthos Island), respectively, are presented. In the analysis, the frequency–magnitude distributions in terms of the Gutenberg–Richter scaling relationship are studied, along with the temporal evolution of the aftershock sequences, as described by the Omori–Utsu formula. The processing of interevent times distribution, based on non-extensive statistical physics, indicates a system in an anomalous equilibrium with long-range interactions and a cross over behavior from anomalous to normal statistical mechanics for greater interevent times. A discussion of this cross over behavior is given for all aftershock sequences in terms of superstatistics. Moreover, the common value of the Tsallis entropic parameter that was obtained suggests that aftershock sequences are systems with very low degrees of freedom. Finally, a scaling of the migration of the aftershock zones as a function of the logarithm of time is discussed regarding the rate strengthening rheology that governs the evolution of the afterslip process. Our results contribute to the understanding of the spatiotemporal evolution of aftershocks using a first principles approach based on non extensive statistical physics suggesting that this view could describe the process within a universal view. Full article

This study presents new insights into gluon transverse momentum distributions through non-extensive statistical mechanics, addressing their implications for QCD phenomenology. The saturation physics and scaling laws present in high-energy collision data are investigated as a consequence of gluon distribution modification in a high-density regime. This analysis explores how these modifications influence observables across different collision systems, such as proton–proton, proton–nucleus, and relativistic heavy-ion collisions. Both particle high- and low-transverse-momentum regions are successfully described in hadron production. Full article

The fracture process of heterogeneous materials is studied here in the framework of the discipline of Non-Extensive Statistical Mechanics. Acoustic emission data provided by an experimental protocol with concrete specimens, plain or fiber-reinforced, under bending are taken advantage of. This innovation of the study lies in the fact that the analysis of the acoustic activity is implemented in terms of the energy content of the acoustic signals rather than of their interevent time or their interevent distance. The Energy Distribution Functions were properly fitted using the expression proposed by Shcherbakov, Kuksenko and Chmelet. This study reveals that the loading and fracture processes of the specific materials are definitely non-additive and non-extensive. It is concluded that the presence of notches is crucial since it assigns non-additivity and non-extensivity from relatively low loading levels due to the early formation of the fracture process zone around the crown of the notch. The values of the Tsallis entropic index, q, that were determined are in very good agreement with the respective ones obtained in previous studies by means of different analysis tools. Finally, a clear correlation between the index q and the average energy content of the acoustic signals is highlighted for the whole range of values of the energy content of the acoustic signals. Full article

We investigate multimodal seismicity by analyzing it as the result of multiple seismic sources. We examine three case studies: the Redoubt and Spurr regions in Alaska, where volcanic and subduction-related seismicity occur, and the Kii Peninsula in Japan, where shallow and deep earthquakes are clearly separated. To understand this phenomenon, we perform spatial, temporal, and magnitude analyses. Our application of non-extensive statistical mechanics shows that multimodal models provide a significantly better fit than unimodal ones. We identify patterns in the distributions of time between events and distances between events using multimodal Tsallis q-gamma distributions. In addition, we use the multimodal Sotolongo–Costa model to analyze the magnitude distribution, which effectively captures the complex interactions that may explain the observed lack of fractality in multimodal seismicity. Full article

Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of q-Statistics. Fast-forward to Constantino Tsallis’ illustrious 80th birthday celebration in 2023, where Deniz Eroglu and Ugur Tirnakli delved into Constantino’s collaborative network, injecting renewed vitality into the project. With hearts brimming with appreciation for Tsallis’ enduring inspiration, Eroglu, Boghosian, Borges, and Tirnakli proudly present this meticulously crafted manuscript as a token of their gratitude. Full article

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment. Full article

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments. Full article

Here, we employ natural time analysis of seismicity together with non-extensive statistical mechanics aiming at shortening the occurrence time window of the Kahramanmaraş-Gazientep M7.8 earthquake. The results obtained are in the positive direction pointing to the fact that after 3 February 2023 at 11:05:58 UTC, a strong earthquake was imminent. Natural time analysis also reveals a minimum fluctuation of the order parameter of seismicity almost three and a half months before the M7.8 earthquake, pointing to the initiation of seismic electrical activity. Moreover, before this earthquake occurrence, the detrended fluctuation analysis of the earthquake magnitude time-series reveals random behavior. Finally, when applying earthquake nowcasting, we find average earthquake potential score values which are compatible with those previously observed before strong ($M\ge 7.1$) earthquakes. The results obtained may improve our understanding of the physics of crustal phenomena that lead to strong earthquakes. Full article

Nonextensive statistical mechanics has developed into an important framework for modeling the thermodynamics of complex systems and the information of complex signals. To mark the 80th birthday of the field’s founder, Constantino Tsallis, a review of open problems that can stimulate future research is provided. Over the thirty-year development of NSM, a variety of criticisms have been published ranging from questions about the justification for generalizing the entropy function to the interpretation of the generalizing parameter q. While these criticisms have been addressed in the past and the breadth of applications has demonstrated the utility of the NSM methodologies, this review provides insights into how the field can continue to improve the understanding and application of complex system models. The review starts by grounding q-statistics within scale-shape distributions and then frames a series of open problems for investigation. The open problems include using the degrees of freedom to quantify the difference between entropy and its generalization, clarifying the physical interpretation of the parameter q, improving the definition of the generalized product using multidimensional analysis, defining a generalized Fourier transform applicable to signal processing applications, and re-examining the normalization of nonextensive entropy. This review concludes with a proposal that the shape parameter is a candidate for defining the statistical complexity of a system. Full article

The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size L is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_h$ and $T_l$ ($T_h>T_l$), respectively. These particles at the extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators ($i=2,\cdots ,L-1$) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier’s law for the heat flux is verified numerically, with the thermal conductivity becoming independent of the lattice size in the limit $L\to \infty$, scaling with the temperature, as $\kappa \left(T\right)\sim T^{-2.25}$, where $T=(T_h+T_l)/2$. Moreover, the thermal conductance, $\sigma (L,T)\equiv \kappa \left(T\right)/L$, is well-fitted by a function, which is typical of nonextensive statistical mechanics, according to $\sigma (L,T)=A{exp}_q(-B{x}^{\eta })$, where A and B are constants, $x=L^{0.475}T$, $q=2.28\pm 0.04$, and $\eta =2.88\pm 0.04$. Full article

The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions. Full article