Nonextensive Parameter Research Articles

New explanation for accelerated expansion and flat galactic rotation curves

Employing the non-additive Tsallis entropy, Ssim A^{beta }, for the large-scale gravitational systems, we disclose that in the cosmological scales both the Friedmann equation and the equation of motion for Newtonian cosmology get modified, respectively. We then derive the modified Newton’s law of gravitation which is valid on large scales. We show that, in the relativistic regime, the modified Friedmann equation admits an accelerated expansion, for a universe filled with ordinary matter, without invoking any kind of dark energy, provided the non-extensive parameter is chosen beta <1/2. In the non-relativistic regime, however, the modified Newton’s law of gravitation can explain the flat galactic rotation curves without invoking particle dark matter provided beta lesssim 1/2. Our study may be regarded as an alternative explanation for the “dark side of the universe”, through modification of the gravitational field equations.

Effect of confining potential on information entropy measures in hydrogen atom: extensive and non-extensive entropy

A spherically confined hydrogen atom has been considered using two different confined potentials such as modified Kratzer and non-spherical oscillator potentials. First, the Schrodinger equation in $$ r $$ -space has been solved and the exact analytical wave functions and energy levels have been obtained. Then, the Renyi entropy and Shannon entropy in $$ r $$ -space have been calculated. In addition, we have numerically calculated the wave functions in $$ p $$ -space by performing Fourier transform. The calculations have been done for different quantum numbers $$ n $$ and $$ l $$ and also quantum size $$ r_{0} $$ . The Bialynicki–Birula–Mycielski inequality is also tested. It is found that this inequality depends on non-extensive parameter $$ q $$ .

Dust-ion-acoustic rogue waves in presence of non-extensive non-thermal electrons

Dust-ion-acoustic (DIA) rogue waves (DIARWs) are investigated in a three component dusty plasma system containing inertialess electrons featuring nonthermal nonextensive distribution as well as inertial warm ions and negatively charged dust grains. A nonlinear Schrödinger equation (NLSE), which governs the conditions of the modulational instability (MI) of DIA waves (DIAWs), is obtained by using the reductive perturbation method. It has been observed from the numerical analysis of NLSE that the plasma system supports both the modulationally stable domain, in which dispersive and nonlinear coefficients of the NLSE have the same signs, and the unstable domain, in which dispersive and nonlinear coefficients of the NLSE have opposite signs, and also supports the DIARWs only in the unstable domain. It is also observed that the basic features (viz., stability of the DIAWs, MI, growth rate, amplitude, width of the DIARWs, etc.) are significantly modified by the related plasma parameters (viz., dust charge state, number density of electron and ion, nonextensive parameter q, nonthermal parameter α, etc.). The present study is useful for understanding the mechanism of the formation of DIARWs in the laboratory and space environments where inertialess mixed distributed electrons can exist with inertial ions and dust grains.

Electron-Acoustic Shock Waves in Cylindrical and Spherical Geometry with Non-Extensive Electrons

We consider nonplanar electron acoustic shock waves composed of stationary ions, cold and non-extensive hot electrons under multiple temperature electrons model in unmagnetized plasma. In this model Modified Korteweg-de Vries–Burger (KdVB) equation is obtained in the cylindrical/spherical coordinates. On the basis of the solutions of KdVB equation, the variation of shock waves features (amplitude, velocity, and width) with different plasma parameters are analyzed. Dissipation effect is introduced in the model by means of kinematic viscosity term. KdVB equation always leads to monotonic solitons and no oscillatory part or peak may appear. It is observed that the combined effect of particle density $$(\alpha )$$, nonextensivity parameter q, electron temperature ratio $$(\theta )$$, and kinetic viscosity $$({{\eta }_{0}})$$ significantly changes the properties of shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyze the soliton features in laboratory and in the space environments.

Three-dimensional Nonlinear Structures in Magnetized Complex Plasmas

A three-dimensional multi-component magneto-plasma system consisting of hybrid nonextensive-nonthermal-distributed electrons, positive ions, and immobile negatively charged dust grains is considered to examine the modulational instability (MI) of dust ion-acoustic waves (DIAWs). The reductive perturbation method, which is valid for small but finite amplitude DIAWs, is employed to derive the (3 + 1)-dimensional nonlinear Schrodinger equation (NLSE). The NLSE leads to the MI of DIAWs as well as the formation of dust ion-acoustic rogue waves (DIARWs), which are formed due to the effects of nonlinearity in the propagation of DIAWs. It is found that the basic features (viz. amplitude and width) of the DIAWs and DIARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as non-extensive (non-thermal) parameter q(α), number densities of plasma species, threshold modulational obliqueness ($${{\theta }_{c}}$$), etc. The application of the results in space and laboratory magneto-plasma system is briefly discussed.

The nonextensive Bose-Einstein condensation and photon gas with parameter transformation

The nonextensive boson system is revisited with the statistical ensemble theory, where the fundamental grand canonical distribution is derived from the equiprobability principle. By recourse to the approach of parameter transformation, one familiar and concise statistical formula for bosons is deduced, in an accurate fashion. Then the Bose-Einstein condensation phenomenon is re-discussed. The results show that the critical temperature is dependent on the nonextensive parameter $ \nu$ , and in the generalized expression of the heat capacity for the condensated phase of boson systems there exists one additional term, obeying the T3 law. By use of the statistical formula, the nonextensive photon gas is also researched. The internal energy and heat capacity for the nonextensive photon gas exhibit a similar dependence on the temperature to the classical photon gas, apart from a coefficient correction dependent on the parameter $ \nu$ . The Gibbs function for the nonextensive photon gas is still zero, showing that the photon field is also at thermal equilibrium, like the situation of classical photon field. The entropy of photon field can be calculated through the integral of the nonextensive quantum statistics formula and can also be derived from the original definition of Tsallis entropy, by recourse to the direct parameter transformation. This seems to indicate the validity of the treatment technique for the nonextensive quantum systems.

The extended uncertainty principle inspires the Rényi entropy

We use the extended uncertainty principle (EUP) in order to obtain the Rényi entropy for a black hole (BH). The result implies that the non-extensivity parameter, appearing in the Rényi entropy formalism, may be evaluated from the considerations which lead to EUP. It is also shown that, for excited BHs, the Rényi entropy is a function of the BH principal quantum number, i.e., the BH quantum excited state. Temperature and heat capacity of the excited BHs are also investigated addressing two phases while only one of them can be stable. In this situation, whereas entropy is vanishing, temperature may take a non-zero positive minimum value, depending on the value of the non-extensivity parameter. The evaporation time of excited BH has also been studied.

Distinct features of Alfvén wave in non-extensive plasmas

Since the time of its discovery, Alfvén wave has been the subject of attention in both theoretical and experimental plasma physics. To date, many different aspects of this wave have been studied using various models. In this study, we adopt linearized Vlasov–Maxwell system and investigate very important characteristics of the wave: electromagnetic field perturbation and Poynting flux, which gives a measure of the electromagnetic energy stored in the field. The plasma which supports the wave is considered to be non-extensive. It is found that the electromagnetic field behaves totally different from the Maxwellian case, and so does the resultant transport of energy. Due to the wide spectrum of the non-extensive parameter q, the results can incorporate a broad range of possibilities which suggest that the energy transport of the wave over short and long distances may somehow be controlled by the non-extensivity of the plasmas.

Violation of Wiedemann-Franz Law for hot hadronic matter created at NICA, FAIR and RHIC energies using non-extensive statistics

We present here the computation of electrical and thermal conductivity by solving the Boltzmann transport equation in relaxation time approximation. We use the $q$-generalized Boltzmann distribution function to incorporate the effects of non-extensivity. The behaviour of these quantities with changing temperature and baryochemical potential has been studied as the system slowly moves towards thermodynamic equilibrium. We have estimated the Lorenz number at NICA, FAIR and the top RHIC energies and studied as a function of temperature, baryochemical potential and the non-extensive parameter, $q$. We have observed that Wiedemann-Franz law is violated for a non-extensive hadronic phase as well as for an equilibrated hadron gas at high temperatures.

Hadronization within the non-extensive approach and the evolution of the parameters

We review transverse momentum distributions of various identified charged particles stemming from high energy collisions fitted by various non-extensive distributions as well as by the usual Boltzmann-Gibbs statistics. We investigate the best-fit formula with the obtained $\chi^2/ndf$ values. We find that the physical mass and $\sqrt{s}$ scaling become more explicit with heavier produced hadrons in both proton-proton and heavy-ion collisions. The spectral shape parameters, in particular the temperature $T$ and the non-extensive Tsallis parameter $q$, do exhibit an almost linear dependence with the centrality-dependence in heavy-ion collisions.

Oblique modulation of electron acoustic waves in nonextensive plasma

In this paper, we have studied the oblique modulation of electron acoustic (EA) waves and formation and properties of envelope solitons in three component plasma consisting of cold electrons, nonextensive hot electrons, and stationary ions. To study the stability criteria of waves, the nonlinear Schrödinger equation (NLSE) is derived. The numerical calculations of the NLSE show the variation of the stability region with different plasma parameters. It reveals that the stability criteria of EA waves depend on the modulation angle θ. The effect of nonextensive parameter q and electron temperature ratio σ on the formation of EA wave envelope excitations has been studied in detail, and the findings obtained here will be beneficial for further astrophysical investigations.

Effect of Dust Charge Fluctuation on Ion Acoustic Waves in a Plasma with Nonextensive Electrons

The linear dispersion for ion acoustic waves (IAWs) including the effects of dust charge fluctuation and electron nonextensivity is derived. It is shown that the presence of nonextensive electrons modifies the charge fluctuation behavior, leading to the dissipative and instability for IAWs. The dependence of the frequency and damping rate of IAWs on the electron nonextensive parameter q is closely to the dust density since it greatly affects the dust charge fluctuation.

Propagation of Solitary Waves and Double-Layers in Electron–Positron Pair Plasmas with Stationary Ions and Nonextensive Electrons

Based on reductive perturbation theory, the nonlinear structure of non-extensive multispecies plasma containing hot electrons, adiabatic cold electrons, cold positrons and ions has been investigated via different nonlinear KdV, mKdV and Gardner’s equations. It is shown that the formation and properties of electron acoustic solitary waves and double-layer can exist in such plasma system depending on some relevant physical parameters such as electron and positron density ratios, electrons temperatures ratio and non-extensive parameter. The existence conditions of these types of waves are extensively discussed. The obtained results may be useful in improving and understanding the propagation of the nonlinear electron waves in space plasma, Earth’s magnetosphere and solar wind.

The nonextensive statistical ensembles with dual thermodynamic interpretations

The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for the limit of large particle number for most normal systems. In this case, Tsallis entropy can be expanded as a function of energy and particle number fluctuation, and thus the power-law forms of the generalized Gibbs distribution and grand canonical distribution can be derived. These new distribution functions can be applied to derive the free energy and grand thermodynamic potential in nonextensive thermodynamics. In order to establish appropriate nonextensive thermodynamic formalism, the dual thermodynamic interpretations are necessary for thermodynamic relations and thermodynamic quantities. By using a new technique of parameter transformation, the single-particle distribution can be deduced from the power-law Gibbs distribution. This technique produces a link between the statistical ensemble and the quasi-independent system with two kinds of nonextensive parameter having quite different physical explanations. Furthermore, the technique is used to construct nonextensive quantum statistics and effectively to avoid the factorization difficulty in the power-law grand canonical distribution.

Study of RbCl quantum pseudodot qubits by using of non-extensive entropies

In this work, an electron which is strongly coupled to the strong electron–phonon (e–p) in RbCl quantum pseudodot qubit is considered. First, we employ the Pekar variational method and obtain the eigenenergies and eigenfunctions of the ground and the first excited states of the system. Then, we have employed three different entropies such as Tsallis, Landsberg–Vedral, and Escort for the system subjected to an applied electric field. In this regard, we have studied the effect of polaronic radius, electric field, e–p coupling strength, and non-extensive parameter. It is found that the entropies oscillate with passing time. The entropies increase with enhancing electric field, e–p coupling strength and decrease with polaronic radius. The results show that the missing information in the RbCl pseudodot qubit can be controlled by changing the system parameters. According to the results, it is deduced that the entropy is an important quantity to display the total storage or missing information in a qubit.

Hadron Spectra Parameters within the Non-Extensive Approach

We investigate how the non-extensive approach works in high-energy physics. Transverse momentum ( p T ) spectra of several hadrons are fitted by various non-extensive momentum distributions and by the Boltzmann–Gibbs statistics. It is shown that some non-extensive distributions can be transferred one into another. We find explicit hadron mass and center-of-mass energy scaling both in the temperature and in the non-extensive parameter, q, in proton–proton and heavy-ion collisions. We find that the temperature depends linearly, but the Tsallis q follows a logarithmic dependence on the collision energy in proton–proton collisions. In the nucleus–nucleus collisions, on the other hand, T and q correlate linearly, as was predicted in our previous work.

Nonperturbative thermodynamic geometry of nonextensive statistics

Following our earlier work on the perturbative thermodynamic geometry of nonextensive quantum and classical gases [H. Mohammadzadeh, F. Adli and S. Nouri, Phys. Rev. E 94 (2016) 062118], we study [Formula: see text]-generalized Bose–Einstein, Fermi–Dirac and classical statistics nonperturbatively. We define [Formula: see text]-generalized polylogarithm functions and evaluate thermodynamics quantities such as internal energy and particle number. We construct the thermodynamic geometry of nonextensive Bose (Fermi) ideal gas and show that the thermodynamic curvature is positive(negative) in full physical range as the same as ordinary statistics. Also, we show that the thermodynamic geometry of nonextensive ideal classical gas is flat, similar to the ordinary one. Therefore, the nonextensive parameter does not change the nature of intrinsic statistical interactions. We argue that the nonextensive boson gas might be more stable than the boson gas due to conjectural interpretation of thermodynamic curvature. In the following, we extract the singular points of thermodynamic curvature of nonextensive Bose gas and relate it to the condensation. We evaluate some thermodynamic quantities such as heat capacities, compressibility and [Formula: see text]-dependent phase transition temperature. We show that the heat capacity is not differentiable at critical temperature, [Formula: see text] which is reduced by increasing nonextensive parameter [Formula: see text]. Moreover, the critical temperature and possibility of condensation is investigated for different values of nonextensive parameter in various dimensions.

Influence of dust-neutral collisional frequency and nonextensivity on dynamic motion of dust-acoustic waves

ABSTRACT Influence of dust-neutral collisional frequency and nonextensivity on the linear and nonlinear dust-acoustic waves is studied in a magnetized collisional dusty plasma, which consists of negatively charged cold dust particles, q-nonextensive hot ions and hot electrons with stationary neutrals considering the dust-neutral collisions. It is observed through linear mode analysis that linear dust-acoustic wave behaves like a damping wave and its damping rate mainly depends on dust-neutral collisional frequency (). The damped Zakharov and Kuznetsov (ZK) equation is obtained employing the reductive perturbation technique. The effects of dust-neutral collisional frequency () and nonextensive parameter (q) are observed on the characteristic features of dust-acoustic solitary waves. Control of dynamic motions for dust-acoustic waves is investigated considering three-dimensional phase portraits, time-series analysis and sensitivity analysis. The parameters , and play vital roles on the control of dynamic motions for dust-acoustic waves in presence of the external periodic force. Our study may be helpful to understand the behavior of dust-acoustic wave in the magnetosphere.

Magnetic susceptibility of graphene in non-commutative phase-space: Extensive and non-extensive entropy

In this work, we consider a non-commutative description of graphene. We have employed extensive and non-extensive entropies to study magnetic susceptibility of graphene in non-commutative phase-space. To this end, we have used the Shannon and Tsallis entropies. According to the obtained results, we have found that the magnetic susceptibility has a positive value by using the Shannon entropy. But, by using the Tsallis entropy, we have obtained both positive and negative values for the magnetic susceptibility of graphene. Also, we have found a transition between positive and negative susceptibility by using the Tsallis entropy which depends on both temperature and non-extensive parameter. There is not any transition by using the Shannon entropy.

Nonextensive Quasiparticle Description of QCD Matter

The dynamics of QCD matter is often described using effective mean field (MF) models based on Boltzmann–Gibbs (BG) extensive statistics. However, such matter is normally produced in small packets and in violent collisions where the usual conditions justifying the use of BG statistics are not fulfilled and the systems produced are not extensive. This can be accounted for either by enriching the original dynamics or by replacing the BG statistics by its nonextensive counterpart described by a nonextensivity parameter q ≠ 1 (for q → 1 , one returns to the extensive situation). In this work, we investigate the interplay between the effects of dynamics and nonextensivity. Since the complexity of the nonextensive MF models prevents their simple visualization, we instead use some simple quasi-particle description of QCD matter in which the interaction is modeled phenomenologically by some effective fugacities, z. Embedding such a model in a nonextensive environment allows for a well-defined separation of the dynamics (represented by z) and the nonextensivity (represented by q) and a better understanding of their relationship.