Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation

Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length distribution of plasmid fragments, after irradiation with very high doses, assuming that the system reaches metaequilibrium. By intensively working out the Grand Canonical Ensemble (used to take into account the variation of the number of base pairs) a simplified expression for Fragment Size Distribution Function (FSDF) was obtained. This expression is dependent on two parameters only, the Tsallis q value and the minimal length of the fragments. Results obtained from fittings to available experimental data were adequate and the characteristic behavior of the shortest fragments was clearly documented and reproduced by the model, a circumstance never verified from theoretical distributions. The results point to the existence of an entropy which characterizes fragmentation processes and depending only on the q entropic index.

Modeling of magnetized collisional plasma sheath with nonextensive electron distribution and ionization source

The properties of an atmospheric-pressure collisional plasma sheath with nonextensively distributed electrons and hypothetical ionization source terms are studied in this work. The Bohm criterion for the magnetized plasma is extended in the presence of an ion–neutral collisional force and ionization source. The effects of electron nonextensive distribution, ionization frequency, ion–neutral collision, magnetic field angle and ion temperature on the Bohm criterion of the plasma sheath are numerically analyzed. The fluid equations are solved numerically in the plasma–wall transition region using a modified Bohm criterion as the boundary condition. The plasma sheath properties such as charged particle density, floating sheath potential and thickness are thoroughly investigated under different kinds of ion source terms, contributions of collisions, and magnetic fields. The results show that the effect of the ion source term on the properties of atmosphericpressure collisional plasma sheath is significant. As the ionization frequency increases, the Mach number of the Bohm criterion decreases and the range of possible values narrows. When the ion source is considered, the space charge density increases, the sheath potential drops more rapidly,and the sheath thickness becomes narrower. In addition, ion–neutral collision, magnetic field angle and ion temperature also significantly affect the sheath potential profile and sheath thickness.

Unstable mode of ion-acoustic waves with two temperature q-nonextensive distributed electrons

The linear characteristics of the unstable mode of ion-acoustic waves are examined in an electrostatic electron-ion plasma composed of streaming hot electrons,non-streaming cold electrons and dynamical positive ions.The plasma under consideration is modeled by using a non-gyrotropic nonextensive q-distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming hot electrons with respect to the other plasma species.In the frame work of kinetic model,a linearized set of Vlasov-Poisson's equations are solved to obtain the analytical expressions for dispersion relation and Landau damping rate.The threshold condition for the unstable ion-acoustic wave is derived to assess the stability of the wave in the presence of nonextensive effects.Growth in the wave spectrum and nontrivial effects of q-nonextensive parameter on the ion-acoustic waves can be of interest for the readers in the regions of Saturns's magnetosphere.

The Burr XII Distribution Family and the Maximum Entropy Principle: Power-Law Phenomena Are Not Necessarily “Nonextensive”

In this paper, we recall for physicists how it is possible using the principle of maximization of the Boltzmann-Shannon entropy to derive the Burr-Singh-Maddala (BurrXII) double power law probability distribution function and its approximations (Pareto, loglogistic.) and extension (GB2…) first used in econometrics. This is possible using a deformation of the power function, as this has been done in complex systems for the exponential function. We give to that distribution a deep stochastic interpretation using the theory of Weron et al. Applied to thermodynamics, the entropy nonextensivity can be accounted for by assuming that the asymptotic exponents are scale dependent. Therefore functions which describe phenomena presenting power-law asymptotic behaviour can be obtained without introducing exotic forms of the entropy.

Instability of Thermally Conducting Self-Gravitating Systems

The gravitational instability of a thermally conducting self-gravitating system permeated by a uniform and oblique magnetic field has been analyzed in the framework of Tsallis’ nonextensive theory for possible mod-ifications in the Jeans’ instability criterion. It is concluded that the instability criterion is indeed modified into one that depends explicitly on the nonextensive parameter. The influence of thermal conductivity on the system stability is also examined.

A new form of Tsallis distribution based on the probabilistically independent postulate

The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. This paper finds that the q-exponential of a sum can be applied as the product of the q- exponential based on the probabilistically independent postulate employed in nonextensive statistical mechanics. Under this framework, a new form of Tsallis distribution is suggested. It shows that the new form of Tsallis distribution can supply the statistical description for the nonequilibrium dynamical property of the Hamiltonian system governed by an arbitrary potential, and it is found to be one potential statistical distribution for the dark matter.

Landau damping of longitudinal oscillation in ultra-relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q →1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.

Ion-Acoustic Shock Waves in Nonextensive Electron-Positron-Ion Plasma

A rigorous theoretical investigation is made of ion-acoustic shock structures in an unmagnetized three-component plasma whose constituents are nonextensive electrons, nonextensive positrons, and inertial ions. The Burgers equation is derived by employing the reductive perturbation method. The effects of electron and positron nonextensivity and ion kinematic viscosity on the properties of these ion-acoustic shock waves are briefly discussed. It is found that shock waves with positive and negative potentials are obtained to depend on the plasma parameters. The entailment of our results may be useful to understand some astrophysical and cosmological scenarios including stellar polytropes, hadronic matter and quark-gluon plasma, protoneutron stars, dark-matter halos, etc., where effects of nonextensivity can play significant roles.

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic （DEA） shock waves and double layers in an unmagnetized, col- lisionless, complex or dusty plasma system are carried out. The plasma system is assumed to be composed of inertial and viscous cold electron fluids, nonextensive distributed hot electrons, Maxwellian ions, and negatively charged stationary dust grains. The standard reductive perturbation technique is used to derive the nonlinear dynamical equations, that is, the nonplanar Burgers equation and the nonplanar further Burgers equation. They are also numerically analyzed to investigate the basic features of shock waves and double layers （DLs）. It is observed that the roles of the viscous cold electron fluids, nonextensivity of hot electrons, and other plasma parameters in this investigation have significantly modified the basic features （such as, polarity, amplitude and width） of the nonplanar DEA shock waves and DLs. It is also observed that the strength of the shock is maximal for the spherical geometry, intermediate for cylindrical geometry, while it is minimal for the planar geometry. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.

Analysis of Nonlinear Dust-Acoustic Shock Waves in an Unmagnetized Dusty Plasma with q-Nonextensive Electrons Where Dust Is Arbitrarily Charged Fluid

The nonlinear propagation of dust-acoustic (DA) shock waves in three-component unmagnetized dusty plasma consisting of nonextensive electrons, Maxwellian ions and arbitrarily charged mobile dust grain has been investigated. It is found that the presence of q-nonextensive electrons and ions can change the nonlinear behavior of shock wave. The standard reductive perturbation method is employed to study the basic features (phase speed, amplitude and width) of DA shock waves (DASWs) which are significantly modified by the presence of Maxwellian ions and nonextensive electrons. The present investigation can be very effective for understanding the nonlinear characteristics of the DASWs in space and laboratory dusty plasmas.

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model

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 q<1.15,CEP moves in the direction of lower temperature and larger quark chemical potential.However,for q>1.15,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(σ^(2)),skewness(S),and kurtosis(k).Our results are generally consistent with the latest experimental data reported,especially for√SNN>19.6 GeV,when q is set to 1.07.

QCD chiral phase transition and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model

We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model that is based on nonextentive statistical mechanics.This new statistics model is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs(BG) statistics(for q→ 1,it returns to the BG case).Based on the nonextensive Polyakov-Nambu-Jona-Lasinio model,we discussed the influence of nonextensive effects on the curvature of the phase diagram at μ=0 and especially on the location of the critical end point(CEP).A new and interesting phenomenon we found is that with an increase in q,the CEP position initially shifts toward the direction of larger chemical potential and lower temperature.However,when q is larger than a critical value qc,the CEP position moves in the opposite direction.In other words,as q increases,the CEP position moves in the direction of smaller chemical potential and higher temperature.This U-turn phenomenon may be important for the search of CEP in relativistic heavy-ion collisions,in which the validity of BG statistics is questionable due to strong fluctuations and long-range correlations,and nonextensive effects begin to manifest themselves.In addition,we calculated the influence of the nonextensive effects on the critical exponents and found that they remain almost constant with q.

Theoretical self-consistency in nonextensive statistical mechanics with parameter transformation

Self-consistency in nonextensive statistical mechanics is studied as a recourse to parameter transformation,where different nonextensive parameters are presented for various theoretical branches.The unification between the first and third choices of the average definition and that between the normal and escort distributions are both examined.The problem of parameter inversion in the generalized H theorem is also investigated.The inconsistency between the statistical ensemble pressure and molecular dynamics pressure can be eliminated.This work also verifies the equivalence of physical temperature and gravitational temperature in nonextensive statistical mechanics.In these parameter transformations,the Tsallis entropy form is observed to remain invariant.

Scale-Invariant Occupancy of Phase Space and Additivity of Nonextensive Entropy S_q

<Abstract>Phase space can be constructed for N equal and distinguishable binary subsystems which are correlated in a scale-invariant manner.In the paper,correlation coefficient and reduced probability are introduced to characterize the scale-invariant correlated binary subsystems.Probabilistic sets for the correlated binary subsys-tems satisfy Leibnitz triangle rule in the sense that the marginal probabilities of N-system are equal to the joint probabilities of the(N-1)-system.For entropic index q=1,nonextensive entropy Sq is shown to be additive in the scale-invariant occupation of phase space.

Electron-acoustic supernonlinear waves and their multistability in the framework of the nonlinear Schrödinger equation

Finite-amplitude supernonlinear electron-acoustic waves(EAWs)are investigated under the nonlinear Schrödinger(NLS)equation in a plasma system that is composed of cold electronfluid,immobile ions and q-nonextensive hot electrons.Using the wave transfiguration,the NLS equation is deduced in a dynamical system.The presence of finite-amplitude nonlinear and supernonlinear EAWs is shown by phase plane analysis.The effects of the nonextensive parameter(q)and the speed of waves(v)on different traveling wave solutions of EAWs are presented.Furthermore,by introducing a small external periodic force in the dynamical system,multistability behaviors of EAWs under the NLS equation are shown for the first time in classical plasmas.

Nonextensive effects on QCD chiral phase transition with a chiral chemical potential

In this study,we investigate the QCD chiral phase diagram in the presence of a chiral chemical potential μ based on nonextensive statistical mechanics.A feature of this new statistic is a dimensionless nonextensivity parameter q,which summarizes all possible effects violating the assumptions of Boltzmann-Gibbs(BG)statistics(when q→1,it returns to the BG case).Within the nonextensive Polyakov-Nambu-Jona-Lasinio model,we find that as μ increases,the critical end point(CEP)in the T-μ plane continues to CEP_(5)in the T-μ plane,and nonextensive effects have a significant impact on the evolution from the CEP to CEP_(5).Generally,with an increase in q,both the CEP and CEP_(5)move in the direction of a lower temperature T and larger chemical potentialμ(μ_(5)).In addition,we find that chiral charge density ngenerally increases with T,μ,μ_(5),and q.Our study may provide useful hints about lattice QCD and relativistic heavy-ion collision experiments.