Nonextensive Parameter Research Articles

Coherent states for generalized uncertainty relations and their cosmological implications

We study coherent states associated with a generalized uncertainty principle (GUP). Our particular focus is on the negative deformation parameter β. We show that the ensuing coherent state can be identified with Tsallis’ probability amplitude with the non-extensivity parameter q being a monotonically increasing function of β. Furthermore, for β < 0, we reformulate the GUP in terms of a one-parameter class of Tsallis entropy based uncertainty relations, which are again saturated by the GUP coherent states. We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study the quasi-classical regime of GUP in terms of non-extensive thermostatistics. We bolster this claim by discussing a generalization of Verlinde’s entropic force and the ensuing implications in the late-inflation epoch. The corresponding dependence of the β parameter on the cosmological time is derived for the reheating epoch. The obtained β is consistent with both values predicted by string-theory models and the naturalness principle.

Twisted dust-acoustic waves in a self-gravitating dusty plasma with nonextensive q-distributed electrons and ions

We have investigated the twisted dust-acoustic waves (TDAWs) in an electrostatic self-gravitating dusty plasma whose electrons and ions are modelled by nonextensive q-distribution function while massive dust particles are Maxwellian distributed. A well-known kinetic theory is employed for this purpose where perturbed distribution function, electrostatic and gravitational potentials are expressed with Laguerre–Gauss functions. The governing equations of kinetic theory are solved together under paraxial approximations. The dispersion relations and instability growth rates are obtained for two situations; a) super-extensivity (q < 1) and b) sub-extensivity (q > 1). Significant modifications concerning the wave frequencies and growth rates are presented with respect to self-gravitation parameter, twist parameter, nonextensive parameter and streaming speed. It is observed that wave frequency and growth rate of TDAWs reduces in the presence of self-gravitating effects. Furthermore, the growth rates exhibit a significant enhancement in amplitude with the increase in twist parameter, q-parameter and streaming speed. Our present results may have applications in interstellar dust clouds and in the dusty plasma environments of Halley’s Comet.

Hadron gas in the presence of a magnetic field using non-extensive statistics: a transition from diamagnetic to paramagnetic system

Non-central heavy-ion collisions at ultra-relativistic energies are unique in producing magnetic fields of the largest strength in the laboratory. Such fields being produced at the early stages of the collision could affect the properties of Quantum Chromodynamics matter formed in the relativistic heavy-ion collisions. The transient magnetic field leaves its reminiscence, which in principle, can affect the thermodynamic and transport properties of the final state dynamics of the system. In this work, we study the thermodynamic properties of a hadron gas in the presence of an external static magnetic field using a thermodynamically consistent non-extensive Tsallis distribution function. Various thermodynamical observables such as energy density (ϵ), entropy density (s), pressure (P) and speed of sound (c s) are studied. Investigation of magnetization (M) is also performed and this analysis reveals an interplay of diamagnetic and paramagnetic nature of the system in the presence of a magnetic field of varying strength. Further, to understand the system dynamics under equilibrium and non-equilibrium conditions, the effect of the non-extensive parameter (q) on the above observables is also studied.

Systematic analysis of the pp collisions at LHC energies with Tsallis function

This work focuses on the study of identified (, , p, and ), strange hadrons (, Λ, ), recorded by CMS, and light nuclei and their anti-nuclei (d, , t, , 3He and ), recorded by ALICE, at , 2.76 TeV, 7 TeV and 13 TeV in pp collision at mid rapidities. The p T distributions of these particles are analyzed using the Tsallis model, which fits the experimental data very well. Several important parameters for studying the characteristics of the medium produced during such collisions are extracted. The effective temperature (T) increases monotonically with increasing particle mass and also with increasing collision energy. The non-extensivity parameter (q) decreases with the mass of the particle. For heavier particles, greater T and smaller q mean that they decouple early from the system and attain equilibrium quickly compared to lighter ones. Furthermore, with an increase in collision energy, the multiplicity parameter N 0 increases.

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter q. Thus, when q tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as q increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for , CEP moves in the direction of lower temperature and larger quark chemical potential. However, for , CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, variance (), skewness (S), and kurtosis (κ). Our results are generally consistent with the latest experimental data reported, especially for , when q is set to .

THDE models with specific cutoffs and correspondence with quintessence field

In this paper, we investigated the general behaviors of the Tsallic holographic dark energy (THDE) model in general relativity. Here, we take the Bianchi [Formula: see text] metric, which is homogeneous and anisotropic. We investigate the THDE models with the Hubble horizon and Granda–Oliveros (GO) cutoffs. We have studied the behavior of a few quantities, such as dark energy density [Formula: see text], matter-energy density [Formula: see text], and skewness parameter [Formula: see text] and discuss their physical significances. In our THDE models, the EoS parameter explains the universe’s evolution based on the value of the non-extensive or Tsallis parameter [Formula: see text]. In addition, we develop the cosmographic parameters like, deceleration parameter [Formula: see text], jerk parameter [Formula: see text], lerk parameter [Formula: see text], snap parameter [Formula: see text] and maxout parameter [Formula: see text]. We have explored the [Formula: see text] plane and the stability analysis of the THDE model by a perturbation method. We have also constructed a correspondence between the THDE model with quintessence. Some physical and geometrical behaviors of the models are also discussed.

A Non-Extensive Statistical Physics View of the Temporal Properties of the Recent Aftershock Sequences of Strong Earthquakes in Greece

Greece is one of Europe’s most seismically active areas. Seismic activity in Greece has been characterized by a series of strong earthquakes with magnitudes up to Mw = 7.0 over the last five years. In this article we focus on these strong events, namely the Mw6.0 Arkalochori (27 September 2021), the Mw6.3 Elassona (3 March 2021), the Mw7.0 Samos (30 October 2020), the Mw5.1 Parnitha (19 July 2019), the Mw6.6 Zakynthos (25 October 2018), the Mw6.5 Kos (20 July 2017) and the Mw6.1 Mytilene (12 June 2017) earthquakes. Based on the probability distributions of interevent times between the successive aftershock events, we investigate the temporal evolution of their aftershock sequences. We use a statistical mechanics model developed in the framework of Non-Extensive Statistical Physics (NESP) to approach the observed distributions. NESP provides a strictly necessary generalization of Boltzmann–Gibbs statistical mechanics for complex systems with memory effects, (multi)fractal geometries, and long-range interactions. We show how the NESP applicable to the temporal evolution of recent aftershock sequences in Greece, as well as the existence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for longer interevent times. The observed behavior is further discussed in terms of superstatistics. In this way a stochastic mechanism with memory effects that can produce the observed scaling behavior is demonstrated. To conclude, seismic activity in Greece presents a series of significant earthquakes over the last five years. We focus on strong earthquakes, and we study the temporal evolution of aftershock sequences of them using a statistical mechanics model. The non-extensive parameter q related with the interevent times distribution varies between 1.62 and 1.71, which suggests a system with about one degree of freedom.

Map of suprathermal onto nonextensive parameters describing Langmuir waves

We propose a polytropic-like index that depends on the concentration and number of degrees of freedom of a gas of charged particles following a nonextensive distribution. An equation of state of the gas is obtained and a dispersion relation describing Langmuir waves is derived. Comparison of the acquired dispersion relation with a previous one, recently deduced in the realm of the Kappa distribution, provides an adiabatic map of suprathermal onto nonextensive parameters. In the isothermal limit, the map recovers a well-known relation between those quantities. The results presented here may be useful for investigating the physics of coupled and weakly interacting systems in the nonextensive framework.

Response Characteristics of Weak Current Stimulated from Coal under an Impact Load and Its Generation Mechanism

Understanding the response law and mechanism of weak currents stimulated from coal under an impact load is significant for the prediction of coal bumps in deep coal mines. In this paper, the system for the weak current measurement of coal under an impact load is established and the response characteristics of weak currents induced by the deformation of coal under an impact load are investigated. Physical models are established to describe the process of charge transfer and explain the generation mechanism of those currents. The results show that a transient current is stimulated from the coal sample when an impact load is applied, and then, the current decays slowly, tending to be a stable value that is slightly greater than the background current. The weak current flows from the loaded volume to the unloaded volume of the coal and increases with the impact velocity in a negative exponential form. Analysis of weak currents using non-extensive entropy shows that the attenuation of the weak current obeys non-extensive statistical mechanics and the non-extensive parameter q is greater than 2. The carriers are mainly electrons, of which the distribution obeys the tip effect that electrons tend to enrich towards the tip of a crack. The generation mechanism of those weak currents induced by coal deformation is the instantaneous movement of electrons under a density difference caused by the tip effect. Research results can provide a new perspective to understand the electric phenomena of coal under an impact load as well as a new method for coal bump prediction.

To the derivation of relativistic hydrodynamic equations for a rarefied non-ideal gas system of high-energy particles in the framework of Tsallis statistics

The paper discusses the construction of non-extensive relativistic dissipative hydrodynamics of an anomalous hadronic fluid on the basis of relativistic kinetic equation, obtained earlier in the context of the Tsallis statistics, characterized by the nonextensivity parameter q, and taking into account correlation effects (by rejecting the standard hypothesis of molecular chaos) in the collision term for heavy ions. It is shown that some specific form of local thermal equilibrium quark-gluon matter is described by a generalized version of the relativistic Yüttner distribution. With the help of this distribution all thermodynamic parameters of state are defined in explicit form. Linear constitutive relations and transport coefficients such as shear viscosity, bulk viscosity and heat conductivity are derived from the linearized collision integral written in the Anderson-Witting form and evaluated using a relaxation time approximation. The designed non-extensive relativistic fluid dynamics is designed to simulate a wide range of phenomena in astrophysics, cosmology and high-energy physics.

Study of two-electron temperature plasma sheath using non-extensive electron distribution in presence of an external magnetic field

In this study, the physics of sheath formation in a collisional two-electron temperature plasma in the presence of an oblique external magnetic field has been investigated. At first, a comparative study among the fluid electron model, Boltzmann electron model, and the non-extensive electron model has been carried out and a suitable range of non-extensive parameter q has been predicted. In the latter part, a collisional two-electron temperature plasma is considered. Both the hot and cold electron densities are described using the non-extensive distribution, whereas cold ions are described by the fluid equations. The properties of the sheath are investigated in different collisional regimes by varying the non-extensive parameter (q) and the hot to cold electron densities and temperatures. The magnetic field inclination angle is varied in the limit 1° ≤ α ≤ 5°. It is observed that electron distribution significantly deviates from Boltzmann distribution for nearly parallel magnetic field. Moreover, collision enhanced flux deposition for highly magnetized case is a significant finding of the study. The results obtained in this study can enhance the understanding of plasma–matter interaction processes where multiple electron groups with near parallel magnetic field are found.

Thermodynamics of asymptotically de Sitter black hole in dRGT massive gravity from Rényi entropy

The thermodynamic properties of the de Rham–Gabadadze–Tolley (dRGT) black hole in the asymptotically de Sitter (dS) spacetime are investigated by using Rényi entropy. It has been found that the black hole with asymptotically dS spacetime described by the standard Gibbs–Boltzmann statistics cannot be thermodynamically stable. Moreover, there generically exist two horizons corresponding to two thermodynamic systems with different temperatures, leading to a nonequilibrium state. Therefore, in order to obtain the stable dRGT black hole, we use the alternative Rényi statistics to analyze the thermodynamic properties in both the separated system approach and the effective system approach. Interestingly, we found that it is possible concurrently obtain positive pressure and volume for the dRGT black hole while it is not for the Schwarzschild-de Sitter (Sch-dS) black hole. Furthermore, the bounds on the nonextensive parameter for which the black hole being thermodynamically stable are determined. In addition, the key differences between the systems described by different approaches, e.g., temperature profiles and types of the Hawking–Page phase transition are pointed out.

Simultaneous Analysis of Midrapidity pT Spectra of Identified Particle Species in Pb + Pb Collisions at snn = 2.76 TeV Using Tsallis Distribution with Transverse Flow

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons in ten groups of centrality of Pb + Pb collisions at snn = 2.76 TeV, measured by the ALICE Collaboration, have been analyzed successfully using both thermodynamically consistent and non-consistent Tsallis distribution functions with transverse flow. The collision centrality dependencies of the extracted parameters of two kinds of Tsallis functions with transverse flow have been investigated. The significantly different behavior (growth rates) of ⟨βT⟩ in regions ⟨Npart⟩ &lt; 71 and ⟨Npart⟩ &gt; 71 with the temperature T0 becoming constant in region ⟨Npart⟩ &gt; 71 has been observed. This could indicate that ⟨Npart⟩ = 71 ± 5 (corresponding to ⟨dNch/dη⟩ = 205 ± 15) is a threshold border value of collision centrality for crossover phase transition from the dense hadronic state to the QGP state (or a mixed state of QGP and hadrons) in Pb + Pb collisions at snn = 2.76 TeV. This conjecture is supported further by the observed, significantly different correlations between T0 and ⟨βT⟩ parameters in the corresponding ⟨βT⟩ &lt; 0.44 and ⟨βT⟩ &gt; 0.44 ranges. The strong positive linear correlation between non-extensivity parameter q for pions and kaons, between q for pions and (anti)protons, and between q for kaons and (anti)protons has been obtained. The parameter q for all studied particle species has proven to be strongly anticorrelated with the average transverse flow velocity, ⟨βT⟩. Quite a large positive linear correlation has been obtained between the q of the studied particle species and temperature parameter T0. Analysis of q versus ⟨Npart⟩ dependencies for the studied particle species suggests that the highly thermalized and equilibrated QGP is produced in central Pb + Pb collisions at snn = 2.76 TeV with ⟨Npart⟩ &gt; 160.

How barrow entropy modifies gravity: with comments on Tsallis entropy

Barrow proposed that the area law of the horizon entropy might receive a “fractal correction” Spropto A^{1+Delta /2} due to quantum gravitational effects, with 0leqslant Delta leqslant 1 measures the deviation from the standard area law. While such a modification has been widely studied in the literature, its corresponding theory of gravity has not been discussed. We follow Jacobson’s approach to derive the modified gravity theory (interpreted as an effective theory), and find that in the stationary case the resulting theory only differs from general relativity by a re-scaled cosmological constant. Consequently in asymptotically flat stationary spacetimes the theory is identical to general relativity. The theory is not applicable when there is no horizon; the multi-horizon case is complicated. We emphasize on the importance of identifying the correct thermodynamic mass in a theory with modified thermodynamics to avoid inconsistencies. We also comment on the Hawking evaporation rate beyond the effective theory. In addition, we show that the Bekenstein bound is satisfied if the thermodynamic mass is used as the energy, up to a constant prefactor. We briefly comment on the Tsallis entropy case as well. Interestingly, for the latter, the requirement that Bekenstein bound holds imposes a lower bound on the non-extensive parameter: delta > 1/2, which unfortunately rules out the previously suggested possibility that the expansion of the universe can accelerate with normal matter field alone.

Universal scaling of kinetic freeze-out parameters across different collision systems at LHC energies* *Supported by the National Natural Science Foundation of China (11905188, 11875143 and 12061141008), the National Key Research and Development Program of China (2016YFE0100900) and the Innovation Fund of Key Laboratory of Quark and Lepton Physics LPL2020P01 (LZ)

In this study, we perform Tsallis Blast-Wave analysis on the transverse momentum spectra of identified hadrons produced in a wide range of collision systems at the Large Hadron Collider (LHC) including pp, pPb, XeXe, and PbPb collisions. The kinetic freeze-out properties varying with event multiplicity are investigated across these systems. We find that the extracted kinetic freeze-out temperature, radial flow velocity, and non-extensive parameter exhibit a universal scaling behavior for these systems with very different geometric sizes, especially when the independent baryon Tsallis non-extensive parameter is considered. This universality may indicate the existence of a unified partonic evolution stage in different collision systems at the LHC energies.

Nonextensive hydrodynamics of boost-invariant plasmas

We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter q. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including q. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function (q rightarrow 1). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter q.

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.

Analysis of Midrapidity pT Distributions of Identified Charged Particles in Pb + Pb Collisions at snn = 5.02 TeV Using Tsallis Distribution with Embedded Transverse Flow

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at snn = 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ2 fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb + Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at snn = 5.02 TeV with the average number of participant nucleons ⟨Npart⟩ &gt; 160. The obtained significantly different growth rates of transverse flow velocity, ⟨βT⟩, in regions ⟨Npart⟩ &lt; 71 ± 7 and ⟨Npart⟩ &gt; 71 ± 7 with the temperature parameter T0 remaining constant within uncertainties in region ⟨Npart⟩ &gt; 71 ± 7 probably indicates that ⟨Npart⟩ ≈ 71 ± 7 (corresponding to ⟨dNch/dη⟩ ≈ 251 ± 20) is a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Pb + Pb collisions at snn = 5.02 TeV. The threshold border value for transverse flow velocity ⟨βT⟩ ≈ 0.46 ± 0.03 (corresponding to ⟨Npart⟩ ≈ 71 ± 7), estimated by us in Pb + Pb collisions at snn = 5.02 TeV, agrees well with the corresponding border value ⟨βT⟩ ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at snn = 5.44 TeV, and with almost constant ⟨βT⟩ values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, GA, USA) in central Au + Au collisions in the snn = 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T0 and ⟨βT⟩ parameters are found to be greatly different in regions ⟨βT⟩ &lt; 0.46 and ⟨βT⟩ &gt; 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at snn = 5.02 TeV.

Effects of a Nonextensive Dust Charge Variation on an Oblique Collision of Dust Acoustic Solitons in a Dusty plasma

In the current study, two-dimensional collision of two dust acoustic solitons in an unmagnetized nonextensive dusty plasma is investigated, including the effect of non-extensive dust charge variation. By using the extended Poincar-Lighthill-Kuo (PLK) method, two Korteweg-de Vries equations that describe the two dust acoustic solitons propagating in two different directions are derived. The phase shifts after a two-dimensional collision of dust acoustic solitons are obtained as well. The effects of parameters of the ratio of ion temperature to electron temperature, the ratio of ion density to electron density and nonextensive parameter of electrons/ions on the phase shifts are discussed with and without dust charge variation. The results show that the phase shift has been significantly influenced by these parameters. Furthermore, the non-extensive dust charge variation has a significant effect on the amplitude, width of a new nonlinear wave, which generates during the oblique collision.

Nonextensive percolation and Lee-Yang edge singularity from nonextensive λϕ3 scalar field theory

We compute the critical exponents for nonextensive λϕ3 scalar field theory for all loop orders and |q−1|<1. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding systems are nonextensive generalizations of their extensive counterparts. For that we employ tools from the recently introduced nonextensive statistical field theory. The results for the nonextensive critical exponents computed depend on the nonextensive parameter q, which encodes global correlations among the degrees of freedom of the system. The extensive results are recovered in the limit q→1. There is an interplay between global correlations and fluctuations, once the nonextensive critical exponents depend on q. This dependence is in agreement with the universality hypothesis.