Search Results (24)

The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the $\kappa$-entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from $\kappa$-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the $\kappa$-formalism, which emerges from the $\kappa$-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on $\kappa$-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the $\kappa$-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized. Full article

It is known that Kaniadakis entropy, a generalization of the Shannon–Boltzmann–Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number $\aleph >0$ that makes Kaniadakis entropy multi-additive, i.e., $S_{\kappa }\left[p^{\mathrm{A}\cup \mathrm{B}}\right]=(1+\aleph )\left(S_{\kappa }\left[p^{\mathrm{A}}\right]+S_{\kappa }\left[p^{\mathrm{B}}\right]\right)$, under the composition of two statistically independent and identically distributed distributions $p^{\mathrm{A}\cup \mathrm{B}}(x,y)=p^{\mathrm{A}}\left(x\right)p^{\mathrm{B}}\left(y\right)$, with reduced distributions $p^{\mathrm{A}}\left(x\right)$ and $p^{\mathrm{B}}\left(y\right)$ belonging to the same class. Full article

The rapid evolution in materials science has resulted in a significant interest in high-entropy alloys (HEAs) for their unique properties. This study focuses on understanding both quaternary and quinary body-centered cubic (BCC) of 12 refractory-based HEAs, and on analysis of their electronic structures, lattice distortions, mechanical, and thermal properties. A comprehensive assessment is undertaken by means of density functional theory (DFT)-based first principles calculations. It is well known that multiple constituents lead to notable lattice distortions, especially in quinary HEAs. This distortion, in turn, has significant implications on the electronic structure that ultimately affect mechanical and thermal behaviors of these alloys such as ductility, lattice thermal conductivity, and toughness. Our in-depth analysis of their electronic structures revealed the role of valence electron concentration and its correlation with bond order and mechanical properties. Local lattice distortion (LD) was investigated for these 12 HEA models. M1 (WTiVZrHf), M7 (TiZrHfW), and M12 (TiZrHfVNb) have the highest LD whereas the models M3 (MoTaTiV), M5 (WTaCrV), M6 (MoNbTaW), and M9 (NbTaTiV) have the less LD. Furthermore, we investigated the thermal properties focusing on Debye temperature (Θ_D), thermal conductivity (κ), Grüneisen parameter (γ_α), and dominant phonon wavelength (λ_dom). The NbTaTiV(M9) and TiVNbHf(M10) models have significantly reduced lattice thermal conductivities (κ_L). This reduction is due to the mass increase and strain fluctuations, which in turn signify lattice distortion. The findings not only provide an understanding of these promising materials but also offer guidance for the design of next-generation HEAs with properties tailored for potential specific applications. Full article

Kaniadakis statistics is a widespread paradigm to describe complex systems in the relativistic realm. Recently, gravitational and cosmological scenarios based on Kaniadakis ($\kappa$-deformed) entropy have been considered, leading to generalized models that predict a richer phenomenology comparing to their standard Maxwell–Boltzmann counterparts. The purpose of the present effort is to explore recent advances and future challenges of Gravity and Cosmology in Kaniadakis statistics. More specifically, the first part of the work contains a review of $\kappa$-entropy implications on Holographic Dark Energy, Entropic Gravity, Black hole thermodynamics and Loop Quantum Gravity, among others. In the second part, we focus on the study of Big Bang Nucleosynthesis in Kaniadakis Cosmology. By demanding consistency between theoretical predictions of our model and observational measurements of freeze-out temperature fluctuations and primordial abundances of ${}^{4}He$ and D, we constrain the free $\kappa$-parameter, discussing to what extent the Kaniadakis framework can provide a successful description of the observed Universe. Full article

The controlled deposition of CoCrFeNiMo${}_{0.2}$ high-entropy alloy (HEA) microparticles was achieved by using laser-induced forward transfer (LIFT). Ultra-short laser pulses of 230 fs of 515 nm wavelength were tightly focused into ∼2.4 μm focal spots on the ∼50-nm thick plasma-sputtered films of CoCrFeNiMo${}_{0.2}$. The morphology of HEA microparticles can be controlled at different fluences. The HEA films were transferred onto glass substrates by magnetron sputtering in a vacuum (${10}^{-8}$ atm) from the thermal spray-coated substrates. The absorption coefficient of CoCrFeNiMo${}_{0.2}$$\alpha \approx 6\times {10}^5$ cm${}^{-1}$ was determined at 600-nm wavelength. The real and imaginary parts of the refractive index $(n+i\kappa )$ of HEA were determined from reflectance and transmittance by using nanofilms. Full article

Human life necessitates high-quality sleep. However, humans suffer from a lower quality of life because of sleep disorders. The identification of sleep stages is necessary to predict the quality of sleep. Manual sleep-stage scoring is frequently conducted through sleep experts’ visually evaluations of a patient’s neurophysiological data, gathered in sleep laboratories. Manually scoring sleep is a tough, time-intensive, tiresome, and highly subjective activity. Hence, the need of creating automatic sleep-stage classification has risen due to the limitations imposed by manual sleep-stage scoring methods. In this study, a novel machine learning model is developed using dual-channel unipolar electroencephalogram (EEG), chin electromyogram (EMG), and dual-channel electrooculgram (EOG) signals. Using an optimum orthogonal filter bank, sub-bands are obtained by decomposing 30 s epochs of signals. Tsallis entropies are then calculated from the coefficients of these sub-bands. Then, these features are fed an ensemble bagged tree (EBT) classifier for automated sleep classification. We developed our automated sleep classification model using the Sleep Heart Health Study (SHHS) database, which contains two parts, SHHS-1 and SHHS-2, containing more than 8455 subjects with more than 75,000 h of recordings. The proposed model separated three classes if sleep: rapid eye movement (REM), non-REM, and wake, with a classification accuracy of 90.70% and 91.80% using the SHHS-1 and SHHS-2 datasets, respectively. For the five-class problem, the model produces a classification accuracy of 84.3% and 86.3%, corresponding to the SHHS-1 and SHHS-2 databases, respectively, to classify wake, N1, N2, N3, and REM sleep stages. The model acquired Cohen’s kappa ($\kappa$) coefficients as 0.838 with SHHS-1 and 0.86 with SHHS-2 for the three-class classification problem. Similarly, the model achieved Cohen’s $\kappa$ of 0.7746 for SHHS-1 and 0.8007 for SHHS-2 in five-class classification tasks. The model proposed in this study has achieved better performance than the best existing methods. Moreover, the model that has been proposed has been developed to classify sleep stages for both good sleepers as well as patients suffering from sleep disorders. Thus, the proposed wavelet Tsallis entropy-based model is robust and accurate and may help clinicians to comprehend and interpret sleep stages efficiently. Full article

The ionosphere has important influences on trans-ionosphere radio propagation. When signals pass through ionospheric irregularities, their amplitude and phase are often attenuated and distorted. In this work, the statistical features of scintillation observed by the Global Navigation Satellite System (GNSS) and low earth orbit (LEO) satellites are investigated with Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) data in solar cycle 24. The amplitude scintillation propagation channel is fitted by the Nakagami-m, α-μ and κ-μ models. The performance is evaluated in terms of root mean square error (RMSE), kurtosis and information entropy. The results reveal that the α-μ model achieves the best performance in all considered scintillation intensities, while the Nakagami-m model achieves better performance under severe scintillation in the GNSS-LEO propagation channels. Full article

The quantitative determination of the current load carrying capability of already loaded structural elements and the possibility to detect proper indices that could be considered as signals for timely warning that the load carrying capacity is exhausted is the subject of this study. More specifically, it aims to explore the possibility of detecting signals that can be considered as indices warning about upcoming fracture and then to compare quantitatively such signals provided by different techniques. The novelty of the present study lies exactly in this quantitative comparison of the pre-failure signals provided by various sensing techniques and various methods of analysis of the experimental data. To achieve this target, advantage is taken of data concerning the acoustic and electrical activities produced while marble specimens are subjected to mechanical loading. The respective signals are detected and recorded by means of the acoustic emissions technique and that of the pressure stimulated currents. The signals detected by the acoustic emissions technique are analyzed in terms of three formulations, i.e., the b-value, the F-function and the parameters variance κ₁, entropy S and entropy under time reversal S_ according to the natural time analysis. The signals detected by the pressure stimulated currents technique are analyzed by means of the intensity of the electric current recorded. The study indicates that all quantities considered provide promising pre-failure indicators. Furthermore, when the specimen is subjected to near-to-failure load levels, the temporal evolution of three of the quantities studied (b-value, F-function, pressure stimulated currents) is governed by a specific power law. The onset of validity of this law designates some differentiation of the damage mechanisms activated. Quantitative differences are observed between the time instants at which this power law starts dictating the evolution of the above parameters, indicating the imperative need for further investigation, despite the quite encouraging results of the present study. Full article

As known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain analytical function $f_{\left\{\pi \right\}}\left(n\right)$ of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters $\left\{\pi \right\}$. It is shown that, when $f_{\left\{\pi \right\}}\left(n\right)$ is related to the solutions of a simple linear difference–differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree $(\kappa ,r)$ known, in the framework of the information theory, as Sharma–Taneja–Mittal entropic form. Full article

The family of cumulative paired $\varphi$-entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s $\kappa$, with the weights being related to the actual choice of $\varphi$. Again, the asymptotic distribution of the corresponding sample ${\kappa }_{\varphi }$ is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel $\varphi$-entropy-related measures are applied to an ordinal time series on the daily level of air quality. Full article

One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is commonly found throughout the Universe, e.g., the solar wind and the Earth’s magnetosphere correspond to natural plasma physics laboratories in which turbulent phenomena can be studied. Our study perspective is born from the method of Horizontal Visibility Graph (HVG) that has been developed in the last years to analyze time series avoiding the tedium and the high computational cost that other methods offer. Here, we build a complex network based on directed HVG technique applied to magnetic field fluctuations time series obtained from Particle In Cell (PIC) simulations of a magnetized collisionless plasma to distinguish the degree distributions and calculate the Kullback–Leibler Divergence (KLD) as a measure of relative entropy of data sets produced by processes that are not in equilibrium. First, we analyze the connectivity probability distribution for the undirected version of HVG finding how the Kappa distribution for low values of $\kappa$ tends to be an uncorrelated time series, while the Maxwell–Boltzmann distribution shows a correlated stochastic processes behavior. Subsequently, we investigate the degree of temporary irreversibility of magnetic fluctuations that are self-generated by the plasma, comparing the case of a thermal plasma (described by a Maxwell–Botzmann velocity distribution function) with non-thermal Kappa distributions. We have shown that the KLD associated to the HVG is able to distinguish the level of reversibility that is associated to the thermal equilibrium in the plasma, because the dissipative degree of the system increases as the value of $\kappa$ parameter decreases and the distribution function departs from the Maxwell–Boltzmann equilibrium. Full article

Random fiber gratings (RFGs) have shown great potential applications in fiber sensing and random fiber lasers. However, a quantitative relationship between the degree of randomness of the RFG and its spectral response has never been analyzed. In this paper, two RFGs with different degrees of randomness are first characterized experimentally by optical frequency domain reflectometry (OFDR). Experimental results show that the high degree of randomness leads to low backscattering strength of the grating and strong strength fluctuations in the spatial domain. The local spectral response of the grating exhibits multiple peaks and a large peak wavelength variation range when its degree of randomness is high. The linewidth of its fine spectrum structures shows scaling behavior with the grating length. In order to find a quantitative relationship between the degree of randomness and spectrum property of RFG, entropy was introduced to describe the degree of randomness induced by period variation of the sub-grating. Simulation results showed that the average reflectivity of the RFG in dB scale decreased linearly with increased sub-grating entropy, when the measured wavelength range was smaller than the peak wavelength variation range of the sub-grating. The peak reflectivity of the RFG was determined by ${\kappa }^{2}L\Delta P$ (where $\kappa$ is the coupling coefficient, $L$ is the grating length, $\Delta P$ is period variation range of the sub-grating) rather than $\kappa L$ when $\Delta P$ is larger than 8 nm in the spatial domain. The experimental results agree well with the simulation results, which helps to optimize the RFG manufacturing processes for future applications in random fiber lasers and sensors. Full article

Nano-size machines are moving from only being topics of basic research to becoming elements in the toolbox of engineers, and thus the issue of optimally controlling their work cycles becomes important. Here, we investigate hydrogen atom-like systems as working fluids in thermodynamic engines and their optimal control in minimizing entropy or excess heat production in finite-time processes. The electronic properties of the hydrogen atom-like system are controlled by a parameter $\kappa$ reflecting changes in, e.g., the effective dielectric constant of the medium where the system is embedded. Several thermodynamic cycles consisting of combinations of iso-$\kappa$, isothermal, and adiabatic branches are studied, and a possible a-thermal cycle is discussed. Solving the optimal control problem, we show that the minimal thermodynamic length criterion of optimality for finite-time processes also applies to these cycles for general statistical mechanical systems that can be controlled by a parameter $\kappa$, and we derive an appropriate metric in probability distribution space. We show how the general formulas we have obtained for the thermodynamic length are simplified for the case of the hydrogen atom-like system, and compute the optimal distribution of process times for a two-state approximation of the hydrogen atom-like system. Full article

Forest managers demand reliable tools to evaluate post-fire vegetation and soil damage. In this study, we quantify wildfire damage to vegetation and soil based on the analysis of burn severity, using multitemporal and multispectral satellite data and species distribution models, particularly maximum entropy (MaxEnt). We studied a mega-wildfire (9000 ha burned) in North-Western Spain, which occurred from 21 to 27 August 2017. Burn severity was measured in the field using the composite burn index (CBI). Burn severity of vegetation and soil layers (CBI_veg and CBI_soil) was also differentiated. MaxEnt provided the relative contribution of each pre-fire and post-fire input variable on low, moderate and high burn severity levels, as well as on all severity levels combined (burned area). In addition, it built continuous suitability surfaces from which the burned surface area and burn severity maps were built. The burned area map achieved a high accuracy level (κ = 0.85), but slightly lower accuracy when differentiating the three burn severity classes (κ = 0.81). When the burn severity map was validated using field CBI_veg and CBI_soil values we reached lower κ statistic values (0.76 and 0.63, respectively). This study revealed the effectiveness of the proposed multi-temporal MaxEnt based method to map fire damage accurately in Mediterranean ecosystems, providing key information to forest managers. Full article

The cubic intermetallic compound Sm${}_3$Co${}_4$Ge${}_{13}$ (space group $Pm\overline{3}n$ ) possesses a cage-like structure composed of Ge and displays an antiferromagnetic transition at $T_N\approx$ 6 K in magnetization, $M\left(T\right)$ , specific heat, $C_p\left(T\right)$ and in thermal conductivity, $\kappa \left(T\right)$. The magnetic transition at $T_N$ is observed to be robust against applied magnetic fields up to 9 T. From the analysis of specific heat, a Sommerfeld coefficient $\gamma$ = 80(2) mJ/mol-Sm K${}^2$ is estimated. The magnetic entropy released at $T_N$ is estimated as lower than that of a doublet, R ln(2). A positive Seebeck coefficient is observed for the thermopower, $S\left(T\right)$. Photoemission spectroscopy reveals distinct electronic character of the near-$E_{\mathrm{F}}$ valence band states arising out of Co($3d$)-Sm($4f$) hybridization and Sm($4f$) electron correlation. The unusual field-independent features in magnetization, specific heat and electrical transport is an indication of the significant correlation between f and d wave functions. Full article