Narrow Results

We study the geometrothermodynamics of black holes within the framework of the five-dimensional Einstein–Gauss–Bonnet (EGB) theory and its various extensions, including Einstein–Maxwell–Gauss–Bonnet (EMGB), the inclusion of a cosmological constant in EMGB and Einstein–Yang–Mills–Gauss–Bonnet (EYMGB). To expand the scope of our research, we utilize Tsallis entropy, an extended form of entropy that surpasses the traditional Boltzmann–Gibbs entropy. We first obtain the relations for the Hawking temperature, specific heat and scalar curvature in terms of Tsallis entropy and then show that incorporating Tsallis entropy into the description of black holes allows us to explore their thermodynamic characteristics beyond conventional limits, providing valuable insight into the stability of the black holes. We analyze that in the scenario of Tsallis entropy, the stability regions and phase transition points of specific heat coincide with the divergence points of scalar curvatures which confirm the consistency of the results. We also provide a comparative examination of our findings for the considered models of black holes. This comparative analysis deepened our understanding of the thermodynamic behavior exhibited by these diverse black holes within the extended EGB framework.

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and Shannon entropies for specific values of its parameters. We develop a number of information-theoretic properties of this generalized entropy and divergence, for instance, the sub-additive property, strong sub-additive property, joint convexity, and information monotonicity. This article presents an exposit investigation on the information-theoretic and information-geometric characteristics of the new generalized entropy and compare them with the properties of the Tsallis and Shannon entropies.

The quantification of the complexity of network is a fundamental problem in the research of complex networks. There are many methods that have been proposed to solve this problem. Most of the existing methods are based on the Shannon entropy. In this paper, a new method which is based on the nonextensive statistical mechanics is proposed to quantify the complexity of complex network. On the other hand, most of the existing methods are based on a single structure factor, such as the degree of each node or the betweenness of each node. In the proposed method, both of the influence of the degree and betweenness are quantified. In the new method, the degree of each node is used as the constitution of the discrete probability distribution. The betweenness centrality is used as the entropic index q. The nodes which have big value of degree and betweenness will be have big influence on the quantification of network’s structure complexity. In order to describe the relationship between the nodes and the whole network more reasonable, a entropy index set is defined in this new method. Therefore, every node’s influence on the network structure will be quantified. When the value of all the elements in the entropic index set is equal to 1, the new structure entropy is degenerated to the degree entropy. It means that the betweenness of each node in the network is equal to each other. And the structure complexity of the network is determined by the node’s degree distribution. In other words, the new structure entropy is a generalization of the existing degree structure entropy of complex networks. The new structure entropy can be used to quantify the complexity of complex networks, especially for the networks which have a special structure.

In this work, application of the recently introduced constant speed kinetic model (CSKM) [A. Zadehgol and M. Ashrafizaadeh, J. Comp. Phys.274 803, (2014); A. Zadehgol, Phys. Rev. E91, 063311 (2015)] in simulating fluid flow through porous media is explored. Discrete forms of Tsallis and Burg entropy functions were first introduced by Boghosian et al. [Phys. Rev. E$68$, 025103, (2003)], in the context of lattice Boltzmann model (LBM). In the CSKM, the virtual particles are concentrated on n-dimensional (nD-) spheres centered at the computational nodes. Using continuous forms of the unconventional entropies of Burg, $h\sim logf$ (for 2D), and Tsallis, $h\sim f^{1-\frac{2}{n}}$ (for nD with $n\ge 3$), the CSKM extends the work of Boghosian et al., in the limit of fixed speed continuous velocities. In this work, the second-order accuracy, efficiency, and thermodynamic consistency of the 2D- and 3D-projections of the 4D-CSKM are explored and numerically verified.

Value-at-risk (VaR) is a crucial subject that researchers and practitioners extensively use to measure and manage uncertainty in financial markets. Although VaR is a standard risk control instrument, there are criticisms about its performance. One of these cases, which has been studied in this research, is the VaR underestimation during times of crisis. In these periods, the non-Gaussian behavior of markets intensifies, and the estimated VaRs by typical models are lower than the real values. A potential approach that can be used to describe the non-Gaussian behavior of return series is the Tsallis entropy framework and nonextensive statistical methods. This paper has used the nonextensive models for analyzing financial markets’ behavior during crisis times. By applying the q-Gaussian probability density function for emerging and mature markets over 20 years, we can see a better VaR estimation than the regular models, especially during crisis times. We have shown that the q-Gaussian models composed of VaR and Expected Shortfall (ES) estimate risk better than the standard models. By comparing the ES, VaR, $q$-VaR and $q$-ES for emerging and mature markets, we see in confidence levels more than 0.98, the outputs of q models are more real, and the $q$-ES model has lower errors than the other ones. Also, it is evident that in the mature markets, the difference of VaR between normal condition and nonextensive approach increases more than one standard deviation during times of crisis. Still, in the emerging markets, we cannot see a specific pattern. The findings of this paper are useful for analyzing the risk of financial crises in different markets.

Considering the boundary effect, we adopt the Tsallis entropy and compute the time evolution of the entropy in low energy reaction system for the first time, dealing with the initial, compression, expansion and fission stages with a consistent method. We find that it rises up in the compression period and reduces slightly after separation, because of the energy exchange between the collective motion and the internal excitation. The research shows that the entropy curves in binary, sequential or direct ternary fissions are distinct, which declares that the entropy may be a novel criterion to study the breakup mechanism of heavy nuclear reactions in low energy.

In this paper, we study temperature fluctuations in the initial stages of the relativistic heavy ion collision using a multiphase transport model. We consider the plasma in the initial stages after collision before it has a chance to equilibrate. We have considered $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ collision with a center-of-mass energy of 200 GeV. We use the nonextensive Tsallis statistics to find the entropic index in the partonic stages of the relativistic heavy ion collisions. We find that the temperature and the entropic index have a linear relationship during the partonic stages of the heavy ion collision. This has already been observed in the hadronic phase. A detailed analysis of the dependence of the entropic index on the system shows that for increasing spacetime rapidity, the entropic index of the partonic system increases. The entropic index also depends on the beam collision energy. The calculation of the entropic index from the experimental data fitting of the transverse momenta deals with the hadronic phase. However, our study shows that the behavior of the entropic index in the initial nonequilibrium stage of the collision is very similar to the behavior of the entropic index in the hadronic stage.

Uncertainties in flavor and mass eigenstates of neutrinos are considered within the majorization approach. Nontrivial bounds reflect the fact that neutrinos cannot be simultaneously in flavor and mass eigenstates. As quantitative measures of uncertainties, both the Rényi and Tsallis entropies are utilized. Within the current amount of experience concerning the mixing matrix, majorization uncertainty relations need to put values of only two parameters, viz. ${𝜃}_{12}$ and ${𝜃}_{13}$. That is, the majorization approach is applicable within the same framework as the Maassen–Uffink relation recently utilized in this context. We also consider the case of detection inefficiencies, since it can naturally be incorporated into the entropic framework. Short comments on applications of entropic uncertainty relations with quantum memory are given.

In statistical theory, the Tsallis entropy is an extended form of the Boltzmann–Gibbs entropy. The dimensionless parameter $\delta$ is employed to state the quantitative difference from the standard scenario. The concepts of Tsallis entropy and the future event horizon are employed in formulating the present new Tsallis holographic dark energy (NTHDE) model. The model attempts to explain the properties of dark energy using the foundation of quantum gravity. The differential equation characterizing the evolution of the NTHDE density parameter is obtained. Expressions stating the dynamic behavior such as equation of state (EoS), deceleration and jerk parameters are obtained in terms of the NTHDE density parameter. For $\delta <1$, the quintessence nature of scalar field could completely characterize the NTHDE. A reconstruction of the scalar field’s dynamics and quintessence potential is attempted. We demonstrate that the diagnosis made by statefinder is adaptive enough to distinguish between quintessence and cosmological constant-based dark energy models. Additionally, observational data obtained from CC$+$ SNIa $+580$ union 2.1 sources are used to evaluate the model’s effectiveness.

In this paper, one discusses the effects of Tsallis entropy on the radial pressure distribution in the proton. Using a damped confinement potential the pressure distribution is obtained from the Tsallis entropy approach, being the entropic-index $\omega$ connected with the proton temperature concerning some transition temperature. Then, the approach allows the study of the proton thermal evolution up to the Quark–Gluon Plasma regime. The von Laue stability condition, arising from the pressure distribution results in positive and negative energy regions. An analogy between the results for the radial pressure distribution and the proton–proton and the antiproton–proton total cross-section is performed. The negative energy region is identified with the odderon exchange while the positive represents the pomeron exchange dominance above some transition energy $\sqrt{s_c}$. The hollowness effect is also discussed in terms of the results obtained and the proposed analogy.

We extend the EM algorithm to overcome its bottleneck, that is to say, the problem of local maxima of the marginal likelihood due to its strong dependence of initial conditions. As an alternative posterior distribution appearing in the so-called Q function, we use the distribution that maximizes the non-extensive Tsallis entropy. The distribution we introduce has a parameter q which represents the non-extensive property of the entropy. We control the parameter q so as to weaken the influence of the initial conditions. In order to investigate its performance, we apply our algorithm to Gaussian mixture estimation problems under some additive noises. In large data limit, we derive the averaged update equations with respect to hyper-parameters, marginal likelihood etc. analytically. Our analysis supports usefulness of our algorithm.

Klimontovich's S theorem serves as a measure of order relative to a reference state for open systems, thereby providing the correct ordering of entropy values with respect to their distance from the equilibrium state. It can also be considered as a generalization of Gibbs' theorem if one of the distributions is associated with the equilibrium state. Here, a nonadditive generalization of S theorem is obtained by the employment of Tsallis entropy. This generalized form is then illustrated by applying it to the Van der Pol oscillator. Interestingly, this generalization procedure favors the use of ordinary probability distribution instead of escort distribution.

We investigate the possibility of discrete groups furnishing a kinematic framework for systems whose thermodynamic behavior may be given by nonadditive entropies. Relying on the well-known result of the growth rate of balls of nilpotent groups, we see that maintaining extensivity of the entropy of a nilpotent group requires using a non-Boltzmann/Gibbs/Shannon (BGS) entropic form. We use the Tsallis entropy as an indicative alternative. Using basic results from hyperbolic and random groups, we investigate the genericity and possible range of applicability of the BGS entropy in this context. We propose a sufficient condition for phase transitions, in the context of (multi-) parameter families of nonadditive entropies.

We have derived a new generalized constraint-based entropy on the basis of the maximum entropy principle. The new entropy which is very similar to, but different from Havrda and Charvat entropy and Tsallis entropy, reduces to the form of Shannon entropy in a limiting case. The characteristics properties of this new entropy have been pointed out.

In this paper we first present a simple axiomatic derivation of Tsallis entropy as an extension of Shannon entropy. As an application we have first study the importance of Tsallis entropy in the statistical characterization of diversity of a population ecosystem. We next study some characteristic properties of an age-structured population on the basis of the Tsallis entropy.

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “${\tau }_q$-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the ${\tau }_q$-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the ${\tau }_q$-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.

In medical image examination, image segmentation is the broadly used method. Currently, the efficient segmentation of mammogram images is the main challenge. Many methods were presented for segmenting the mammogram images, but the results are not satisfactory. In this paper, an efficient segmentation of mammogram images-based Multilevel Thresholding (MLT) method is proposed. Initially, the preprocessing step is executed for eliminating the unnecessary noises. For gaining the useful features from the mammogram images, mammogram image segmentation is carried out using multilevel thresholding method. In this paper, a novel Multi-Objective Emperor Penguin Optimization (MOEPO) algorithm is proposed for searching the multilevel greatest thresholds that segment the images into background and objects. The objective functions of the MLT are Otsu’s method, Kapur and Tsallis entropy. The effectiveness of the proposed method is analyzed using several performances evaluating metrics, like PSNR, FSIM and SSIM. The experimental outcomes show that the performance of the proposed technique is superior to other state-of-the-art methods. The proposed technique is likened to three existing models, viz. ScPSO-MT, Double Threshold and IWO-SUSAN. The SSIM of the proposed technique is 24.99%, 27.83% and 26.95% better than ScPSO-MT, Double Threshold and IWO-SUSAN existing approaches. The PSNR of the proposed technique is 25.27%, 40% and 50.74% better than ScPSO-MT, Double Threshold and IWO-SUSAN approaches. The FSIM of the proposed technique is 28.57%, 34.12% and 34.12% better than ScPSO-MT, Double Threshold and IWO-SUSAN methods.

We describe the evolution of the early and late universe from thermodynamic considerations, using the generalized nonextensive Tsallis entropy with a variable exponent. A new element in our analysis is the inclusion of a bulk viscosity in the description of the cosmic fluid. Using the generalized Friedmann equation, a description of the early and the late universe is obtained.

The proposed model is a study of the nature of dark energy through nonextensive Tsallis entropy. The method is based on the Karolyhazy relation which is a combined idea from quantum physics and general relativity. Dark energy is the energy density of quantum fluctuations in spacetime. This is the key idea behind proposing agegraphic dark energy (ADE) models here. The parameter $\delta$ is used to measure the quantitative distinction from the standard scenario. To look at the cosmological implications of the hypothesized dark energy model, as well as the expansion of the universe filled with zero pressure matter and the resulting dark energy alternatives, the role of IR cutoff is played by age of the universe. The dynamic behavior of dark energy density parameter is carried out. The expressions for the equation of state parameter and deceleration parameter are obtained. The analysis is performed by taking into account a no flow as well as a flow of energy among the dark matter and dark energy sectors of the universe.

This paper presents a novel fatigue crack monitoring method for steel specimens based on the smoothness priors method (SPM) and Tsallis entropy (TE) of strain measurements. The aim of the study is to detect initiation of a crack in steel specimens and subsequently to monitor its propagation under the fatigue load, based on real-time strain measurements. The nonlinear dynamic response of the structure was exploited since it degrades due to the initiation and subsequent propagation of the crack under the external dynamic excitation. The proposed method was experimentally validated. Here, the SPM is applied to decomposing the structural strain response into a nearly-stationary (NS) component and a low frequency aperiodic trend (LFAT) component. Features associated with crack initiation can be extracted from the NS component. The LFAT component, on the other hand, can be used to identify crack propagation. To tackle the singularity of the structural responses associated with a crack, the TE of the NS component was used in detection and monitoring of the crack in the steel specimen. Two other techniques, namely, acoustic emission (AE) sensor and crack opening displacement (COD) gauge were used for the purpose of calibration and comparison. The results show remarkable resemblance in terms of crack initiation and propagation identification exhibited by all three types of sensors, highlighting the potential of the proposed method for real-time detection and subsequent monitoring of crack propagation in steel structures.