Nonextensive Entropy Research Articles

Modified entropies as the origin of generalized uncertainty principles

The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with S+ and S− entropies are negative and positive respectively. This allows us to explore various possibilities in the search of physical implications. We conclude that non-extensive statistics constitutes a signature of quantum gravity.

Entropy and the arrow of time in population dynamics

The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing state that is extensively used in population genetics models. We will consider the Moran process as a paradigm for this class, and will extend our discussion to other models outside this class. We will also discuss the relation between non-extensive entropies in physics and epistasis (i.e., when the effects of different alleles are not independent) and the role of symmetries in population genetic models.

The q-deformed heat equation and q-deformed diffusion equation with q-translation symmetry

In this paper we consider the discrete heat equation with a certain non-uniform space interval which is related to q-addition appearing in the non-extensive entropy theory. By taking the continuous limit, we obtain the q-deformed heat equation. Similarly, we obtain the solution of the q-deformed diffusion equation

Non-extensive entropy and fragment–asperity interaction model for earthquakes

In this study, we developed a fragment–asperity interaction model for earthquakes. Based on Tsallis entropy, this model can provide mathematical expression for the non-extensive entropy of fragments and asperities in the gouge area. From a statistical physics perspective, we hypothesized that non-extensive entropy decreases with energy relaxation after crustal rupture (i.e., following an earthquake). By using a windowing process, the non-extensive entropy value was monitored for three relatively recent earthquakes: the 2009 M6.1 L’Aquila (Italy) earthquake, 2011 M9.0 Tohoku (Japan) megathrust earthquake, and 2016 M7.8 Kaikoura (New Zealand) earthquake. The results support our hypothesis and suggest that the non-extensive entropy formula obtained in this study can provide a good characterization of seismicity for a given area.

Poincaré Plot Nonextensive Distribution Entropy: A New Method for Electroencephalography (EEG) Time Series.

As a novel form of visual analysis technique, the Poincaré plot has been used to identify correlation patterns in time series that cannot be detected using traditional analysis methods. In this work, based on the nonextensive of EEG, Poincaré plot nonextensive distribution entropy (NDE) is proposed to solve the problem of insufficient discrimination ability of Poincaré plot distribution entropy (DE) in analyzing fractional Brownian motion time series with different Hurst indices. More specifically, firstly, the reasons for the failure of Poincaré plot DE in the analysis of fractional Brownian motion are analyzed; secondly, in view of the nonextensive of EEG, a nonextensive parameter, the distance between sector ring subintervals from the original point, is introduced to highlight the different roles of each sector ring subinterval in the system. To demonstrate the usefulness of this method, the simulated time series of the fractional Brownian motion with different Hurst indices were analyzed using Poincaré plot NDE, and the process of determining the relevant parameters was further explained. Furthermore, the published sleep EEG dataset was analyzed, and the results showed that the Poincaré plot NDE can effectively reflect different sleep stages. The obtained results for the two classes of time series demonstrate that the Poincaré plot NDE provides a prospective tool for single-channel EEG time series analysis.

New Tsallis agegraphic dark energy

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 [Formula: see text] 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.

Electric-field-dependent bimodal distribution functions for electrons in argon, xenon, and krypton owing to the Ramsauer-Townsend minima in the electron-atom momentum-transfer cross sections

This paper considers solutions of the linear Fokker-Planck equation for the steady velocity distribution functions of electrons dilutely dispersed in an excess of either argon, xenon, or krypton. Owing to the large Ramsauer-Townsend minima in the electron-atom momentum-transfer cross sections for these atoms, the steady electron distribution, often referred to as the Davydov distribution, exhibits a bimodal distribution which varies dramatically with the strength of the external electric field. This effect provides a unique verification of the location and shape of the Ramsauer-Townsend minima in the cross sections. It is anticipated that current experimental techniques that probe the details of nonequilibrium electron distributions will verify the results reported in this paper. In addition, these nonequilibrium, non-Maxwellian distributions cannot be rationalized in terms of either the Gibbs-Boltzmann entropy nor the Tsallis nonextensive entropy.

A new method of conflicting evidence management based on non-extensive entropy and Lance distance in uncertain scenarios

Handing uncertain information is one of the research focuses currently. For the sake of great ability of handing uncertain information, Dempster-Shafer evidence theory (D-S theory) has been widely used in various fields of uncertain information processing. However, when highly contradictory evidence appears, the results of the classical Dempster combination rules (DCR) can be counterintuitive. Aiming at this defect, by considering the relationship between the evidence and its own characteristics, the proposed method is a new method of conflicting evidence management based on non-extensive entropy and Lance distance in uncertain scenarios. Firstly, the Lance distance function is used to measure the degree of discrepancy and conflict between evidences, and the credibility of evidence is expressed by matrix. Introducing non-extensive entropy to measure the amount of information about evidence and express the uncertainty of evidence. Secondly, the discount coefficient of the final fusion evidence is measured by considering the credibility and uncertainty of the evidence, and the original evidence is modified by the discount coefficient. Then, the final result is obtained by evidence fusion with DCR. Finally, two numerical examples are provided to illustrate the efficiency of the proposed method, and the utility of our work is demonstrated through an application of the active lane change to avoid obstacles to the autonomous driving of new energy vehicles. The proposed method has a better identification accuracy, reaching 0.9811.

Quintessence model of Tsallis holographic dark energy

In order to apply entropy relations and holography to the entire universe, which is a gravitationally nonextensive framework, for consistency one should apply the standard definition for the universe horizon entropy, specifically Tsallis nonextensive entropy. The model of Tsallis holographic dark energy quantified by a new dimensionless parameter δ, which is a generalization of original holographic dark energy is an endeavour for testing the idea of dark energy inside the structure of holographic principle and entropy formalism. The Tsallis parameter δ decides the principle property of the Tsallis holographic dark energy. With the suitable choice of dimensionless parameter δ, this article attempts to analyse the behaviour of Tsallis holographic dark energy using the Tsallis entropy notion. The choice of δ<1 describes completely the quintessence behaviour of Tsallis holographic dark energy. The dynamics of the scalar field as well as potential of the quintessence is reconstructed for the choices of δ<1.

On superstatistics and black hole quasinormal modes

It is known that using Boltzmann-Gibbs statistics, Bekenstein-Hawking entropy SHB, and the quasinormal modes of black holes, one finds that the lowest value of spin is jmin=1. In this paper, we determine jmin, using non-extensive entropies that depend only on the probability (known as Obregon's entropies and have been derived from superstatistics). We also calculate jmin for a set of non-extensive entropies that have free parameters and are written in terms of SBH. We find that jmin depends on the area and the non-extensive parameter.For the non-extensive entropies that only depend on the probability, we find that the modification is only present for micro black holes. For classical black holes the results are the same as for the Boltzmann-Gibbs statistics.

Self-Adaptive Image Thresholding within Nonextensive Entropy and the Variance of the Gray-Level Distribution.

In order to automatically recognize different kinds of objects from their backgrounds, a self-adaptive segmentation algorithm that can effectively extract the targets from various surroundings is of great importance. Image thresholding is widely adopted in this field because of its simplicity and high efficiency. The entropy-based and variance-based algorithms are two main kinds of image thresholding methods, and have been independently developed for different kinds of images over the years. In this paper, their advantages are combined and a new algorithm is proposed to deal with a more general scope of images, including the long-range correlations among the pixels that can be determined by a nonextensive parameter. In comparison with the other famous entropy-based and variance-based image thresholding algorithms, the new algorithm performs better in terms of correctness and robustness, as quantitatively demonstrated by four quality indices, ME, RAE, MHD, and PSNR. Furthermore, the whole process of the new algorithm has potential application in self-adaptive object recognition.

The use of the Pearson differential equation to test energetic distributions in space physics as Kappa distributions; implication for Tsallis nonextensive entropy: II

The use of the Pearson differential equation to test energetic distributions in space physics as Kappa distributions; implication for Tsallis nonextensive entropy: II

Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data.

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an -mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect.

This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.

Non-extensive thermodynamic entropy to predict the dynamics behavior of COVID-19

The current world observations in COVID-19 are hardly tractable as a whole, making situations of information to be incompleteness. In pandemic era, mathematical modeling helps epidemiological scientists to take informing decisions about pandemic planning and predict the disease behavior in the future. In this work, we proposed a non-extensive entropy-based model on the thermodynamic approach for predicting the dynamics of COVID-19 disease. To do so, the epidemic details were considered into a single and time-dependent coefficients model. Their four constraints, including the existence of a maximum point were determined analytically. The model was worked out to give a log-normal distribution for the spread rate using the Tsallis entropy. The width of the distribution function was characterized by maximizing the rate of entropy production. The model predicted the number of daily cases and daily deaths with a fairly good agreement with the World Health Organization (WHO) reported data for world-wide, Iran and China over 2019-2020-time span. The proposed model in this work can be further calibrated to fit on different complex distribution COVID-19 data over different range of times.

Observational constraints on Tsallis modified gravity

ABSTRACT The thermodynamics-gravity conjecture reveals that one can derive the gravitational field equations by using the first law of thermodynamics and vice versa. Considering the entropy associated with the horizon in the form of non-extensive Tsallis entropy, S ∼ Aβ here, we first derive the corresponding gravitational field equations by applying the Clausius relation δQ = TδS to the horizon. We then construct the Friedmann equations of Friedmann-Lemaître-Robertson-Walker Universe based on Tsallis modified gravity (TMG). Moreover, in order to constrain the cosmological parameters of TMG model, we use observational data, including Planck cosmic microwave background, weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results indicate that TMG model with a quintessential dark energy is more compatible with the low redshift measurements of large scale structures by predicting a lower value for the structure growth parameter σ8 with respect to ΛCDM model. This implies that TMG model would slightly alleviate the σ8 tension.

Generalized Poisson ensemble

A generalized Poisson ensemble is constructed using the maximum entropy principle based on the non-extensive entropy. It is found that the correlations which are introduced among the eigenvalues lead to statistical distributions with heavy tails. As a consequence, long-range statistics, measured by the number variance, show super-Poissonian behavior and the short-range ones, measured by the nearest-neighbor-distribution show, with respect to Poisson, enhancement at small and large separations. Potential applications were found for the sequence data of protein and DNA, which display good agreement with the model. In particular, the ensuing parameter λ of the generalized Poisson ensemble can be utilized to facilitate protein classification.

Study of Extensive and Nonextensive Entropy of RbCl Quantum Well Qubit in an Asymmetric Gaussian Potential

We have presented extensive and nonextensive entropy of RbCl quantum well qubits (QWQ). To this end, we have considered an electron that is coupled to the LO-phonon in RbCl quantum well to determine the energy eigenvalues and eigenfunctions of the ground and first excited states of the system using the Pekar variational method. Here, we have used extensive and nonextensive entropies like Shannon and Tsallis to study decoherence of RbCl QWQ for different parameters. Our results show that the entropies have the oscillatory periodic evolution as a function of time due to the form of the confinement potential. According to the obtained results, we can see that the entropies oscillate under a sinusoidal envelope with enhancing the confinement parameters. These results may be very helpful in the transmission of information in the nanostructure.

Jeans Instability of a Protoplanetary Circular Disk Taking into Account the Magnetic Field and Radiation in Nonextensive Tsallis Kinetics

Within the framework of Tsallis nonextensive statistics, the criteria for the Jeans gravitational instability are derived for a self-gravitating protoplanetary disk, whose substance consists of a mixture of a conducting ideal q-gas and modified radiation of a photon gas. The instability criteria are derived from the corresponding dispersion relations written for both neutral disk matter and magnetized plasma with modified blackbody radiation. The thermodynamics of a photon gas are constructed based on the nonextensive Tsallis quantum entropy, which depends on the deformation parameter. It is shown that blackbody q-radiation can stabilize the state of a nonextensive medium for a purely gaseous disk, and for an electrically conducting disk, the Jeans instability criterion is modified by the magnetic field and radiation pressure only in the transverse propagation mode of the disturbance wave.

Nonextensive black hole entropy and quantum gravity effects at the last stages of evaporation

We analyze the generalized uncertainty principle (GUP) impact onto the nonextensive black hole thermodynamics by using R\'enyi entropy. We show that when introducing GUP effects, both R\'enyi entropy and temperature associated with black holes have finite values at the end of the evaporation process. We also study the sparsity of the radiation, associated with R\'enyi temperature, and compare it with the sparsity of Hawking radiation. Finally, we investigate GUP modifications to the sparsity of the radiation when GUP effects are introduced into R\'enyi temperature.