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1.
The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the entropies S BG ≡ −k ∑ i = 1 W p i ln p i and S q ≡ k (1−∑ i = 1 W p i q )/(q−1) (q∊ℜ S 1 = S BG ). Through them we revisit the concept of additivity, and illustrate the (not always clearly perceived) fact that (thermodynamical) extensivity has a well defined sense only if we specify the composition law that is being assumed for the subsystems (say A and B). If the composition law is not explicitly indicated, it is tacitly assumed that A and B are statistically independent. In this case, it immediately follows that S BG (A+B) = S BG (A)+S BG (B), hence extensive, whereas S q (A+B)/k = [S q (A)/k]+[S q (B)/k]+(1−q)[S q (A)/k][S q (B)/k], hence nonextensive for q ≠ 1. In the present paper we illustrate the remarkable changes that occur when A and B are specially correlated. Indeed, we show that, in such case, S q (A+B) = S q (A)+S q (B) for the appropriate value of q (hence extensive), whereas S BG (A+B) ≠ S BG (A)+S BG (B) (hence nonextensive). We believe that these facts substantially improve the understanding of the mathematical need and physical origin of nonextensive statistical mechanics, and its interpretation in terms of effective occupation of the W a priori available microstates of the full phase space. In particular, we can appreciate the origin of the following important fact. In order to have entropic extensivity (i.e., lim N→∞ S(N)/N < ∞, where N≡ numberof elements of the system), we must use (i) S BG , if the number W eff of effectively occupied microstates increases with N like W {{eff}}∼ W ∼ μ N (μ ≥ 1); (ii) S q with q = 1−1/ρ, if W {{eff}}∼ N^ρ < W (ρ ≥ 0). We had previously conjectured the existence of these two markedly different classes. The contribution of the present paper is to illustrate, for the first time as far as we can tell, the derivation of these facts directly from the set of probabilities of the W microstates.  相似文献   

2.
By employing the reductive perturbation technique, nonlinear cylindrical and spherical Korteweg–de Vries Burgers (KdVB) equation is derived for ion acoustic shock waves in an unmagnetized electronegative plasma. The latter is composed of warm positive and warm negative ions as well as q-distributed nonextensive electrons. Numerically, the modified KdVB equation is solved to examine the impact of nonthermal electrons on the profiles of nonplanar fast ion acoustic shocks. With the help of experimental parameters, it is found that the variations of different quantities, like q (nonextensive parameter), α (the negative-to-positive ion mass ratio), μ (the electron-to-positive ion density ratio) and θ i (the positive ion-to-electron temperature ratio), η i0,n0 (the positive/negative ion viscosities) significantly modify the propagation characteristics of nonplanar shocks in electronegative plasmas. The relevance to a laboratory experiment is highlighted, where positive and negative ions are present.  相似文献   

3.
Korteweg-de Vries (KdV) equation for electrostatic ion acoustic wave in a three component plasma containing positive and negative ions along with the nonextensive electrons is derived. Fast and slow ion acoustic modes which propagate with different velocities are excited. The effects of variation of quantities like q (nonextensive parameter), Q (mass ratio of positive to negative ion), μ (electron to positive ion number density ratio), θ i (positive ion to electron temperature ratio) and θ n (negative ion to electron temperature ratio) have been presented for fast and slow ion acoustic modes. Both compressive and rarefactive solitons are observed. It is found that the solitary excitations strongly depend on the mass and density ratios of the positive and negative ions as well as on nonextensive electron parameter.  相似文献   

4.
The nonlinear propagation of ion-acoustic waves is studied in an unmagnetized collissionless electronegative plasma, whose constituents are the inertial warm positive/negative ions and q-distributed nonextensive electrons. The latter have strong impact on the linear dispersion relation. However, for nonlinear analysis, a reductive perturbation technique is employed to derive a Korteweg-de Vries (KdV) equation accounting for nonthermal electrons in nonplanar geometries. Numerically, the effects of various plasma parameters, such as, the nonextensive parameter (q), the negative-to-positive ion mass ratio (α), the electron-to-positive ion number density ratio (μ), the positive ion-to-electron temperature ratio (θ i ) and negative ion-to-electron temperature ratio (θ n ), have been examined on the nonplanar compressive/rarefactive fast ion-acoustic solitons (where the wave phase speed is taken as λ>1). The relevance of our findings involving plasma wave excitations should be useful both for space and laboratory plasmas, where two distinct groups of ions besides the electrons, are present.  相似文献   

5.
Nonlinear propagation of dust-acoustic waves in an unmagnetized dusty plasma consisting of negatively charged mobile dust, nonextensive ions following nonextensive q-distribution and two distinct temperature superthermal electrons following superthermal kappa distribution each, is investigated by employing lower and higher order nonlinear equations, namely the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV) and the Gardner equations. The characteristic features of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two superthermal temperature electrons and ions nonextensivity on the basic characteristics of DA K-dV, mK-dV and Gardner solitons have also been investigated. It has been found that the DA Gardner solitons exhibit either negative or positive potential solitons only for q<q c where, q c is the critical value of the nonextensive parameter q. The possible applications of our results in understanding the localized nonlinear electrostatic structures existing in solar atmosphere, Saturn’s magnetosphere etc. (where the tails of the high energetic particles at different temperatures follow power-law like distribution) are also briefly discussed.  相似文献   

6.
Properties of dust-ion acoustic solitary waves (DIASWs) in dusty plasmas composed of nonextensive electrons, cold fluid ions and stationary dust particles are investigated. The possibility of soliton formation and the effect of nonextensivity of the electron distribution on the soliton characters are studied using the pseudo-potential method. Regions of parameters in which a solitary wave can be propagated in the plasma is analyzed too. It is found that the solitary excitations strongly depend on the electron-ion density ratio (μ), Mach numbers (M) as well as the nonextensive parameter (q). It is shown that the domain of allowed Mach numbers depends drastically on the plasma parameters and especially on the electron nonextensivity. It is found that beyond a threshold value of the nonextensive parameter (q), dust-ion acoustic solitons are admitted.  相似文献   

7.
Theoretically the propagation of two ion acoustic soliton interaction in a three component collisionless unmagnetized plasma which consists of electrons, positrons and cold ions, has been investigated here by employing reductive perturbation technique. In this study, q distributed electrons and Maxwell-Boltzmann distributed positrons are considered and Korteweged-de Vries (KdV) equation is derived. The KdV equation is solved to get two soliton solution by using Hirota bilinear method. The effects of the q distributed electrons on the profiles of two soliton structures and the corresponding phase shifts are investigated. It is observed that both the nonextensive parameter (q) and the ratio of positrons density and electron density (p=n p0/n e0), play a significant role in the formation and existence of two soliton and also in the nature of their phase shifts.  相似文献   

8.
The instability of dust ion acoustic waves (DIAWs) driven by ions and electrons with different drift velocities in an unmagnetized, collisionless, isotropic dusty plasma was investigated. The electrons, ions and dust particles are assumed to be the generalized q-nonextensive distributions. The spectral indices of the q-distributions for the three plasma components are different from each other. Based on kinetic theory, the dispersion relation and the instability growth rate of DIAWs are obtained. It is found that the presence of the nonextensive distribution electrons and ions significantly modify the domain of the instability growth rate, as well as the ion-electron density ratio (ρ) and drifting-thermal velocity ratio (u i0/v Te ). In reverse, the index of dust grains has nearly no any effect on the instability growth rate. Furthermore, the effects of these parameters on the growth rate have also been discussed in detail.  相似文献   

9.
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10.
There is a controversy in the area of nonextensive statistical mechanics regarding the form of the expectation value of a physical quantity. Two definitions have been discussed in the literature: one is the ordinary definition and the other is the normalized q-expectation value associated with the escort distribution. Here, it is proved that the normalized q-expectation value is the correct one to be employed. The Shore-Johnson theorem is used to show that the formalism with the normalized q-expectation value is theoretically consistent with minimum cross entropy principle, whereas the ordinary expectation value has to be excluded.  相似文献   

11.
The long-time development of self-gravitating gaseous astrophysical systems (in particular, the evolution of the protoplanet accretion disk) is mainly determined by relatively fast processes of the collision relaxation of particles. However, slower dynamical processes related to force (Newton or Coulomb) interactions between particles should be included (as q-collisions) in the nonextensive kinetic theory as well. In the present paper, we propose a procedure to include the Newton self-gravity potential and the centrifugal potential in the near-equilibrium power-like q-distribution in the phase space, obtained (in the framework of nonextensive statistics) by means of the modified Boltzmann equation averaged with respect to an unnormalized distribution. We show that if the power distribution satisfies the stationary q-kinetic equation, then the said equation imposes clear restrictions on the character of the long-term force field and on the possible dependence of hydrodynamic parameters of the coordinates: it determines those parameters uniquely. We provide a thermodynamic stability criterion for the equilibrium of the nonextensive system. The results allow us to simulate the evolution of gaseous astrophysical systems (in particular, the gravitational stability of rotating protoplanet accretion disks) more adequately.  相似文献   

12.
It is suggested that the quiet day daily magnetic variation in the polar cap region, Sqp, results partly from the short-circuit effect of the magnetotail current by the polar ionosphere. This implies that there is an inward field-aligned current from the dawnside magnetopause to the forenoon sector of the auroral oval (positively charged) and an outward field-aligned current to the duskside magnetopause from the afternoon sector of the oval (negatively charged), together with the ionospheric (Pedersen and Hall) currents. The distribution of the magnetic field vectors of both combined current systems agrees with the observed Sqpvector distribution. The space charges provide an electric field distribution which is similar to that which has been observed by polar orbiting satellites.  相似文献   

13.
The head-on collision between two electron-acoustic solitary waves (EASWs) in an unmagnetized plasma is investigated, including a cold electrons fluid, hot electrons, obeying a nonextensive distribution and stationary ions. By using the extended Poincaré-Lighthill–Kuo (PLK) perturbation method, the analytical phase shifts following the head-on collision are derived. The effects of the ratio of the number density of hot electrons to the number density of cold electrons α, and the nonextensive parameter q on the phase shifts are studied. It is found that q and the hot-to-cold electron density ratio significantly modify the phase shifts.  相似文献   

14.
On moderately disturbed days when substorms occur frequently, the quiet day daily variation in the polar region (Sqp) is enhanced. On such days, however, the quiet day variation along the dip equator appears to be suppressed, as well as being superposed with ‘fluctuations’.It is suggested that the enhancement of Sqp is related to a partial suppression of the equatorial electrojet. The asymmetric ring current also causes an apparent suppression of the electrojet.On the other hand, the substorm-associated electric field which drives the eastward current in the auroral and subauroral zone (causing positive bays) in the afternoon sector appears to enhance the equatorial electrojet.Thus, magnetic variations along the dip equator are influenced by a number of processes in the magnetosphere.  相似文献   

15.
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16.
Cosmic acceleration is investigated through a kink-like expression for the deceleration parameter (q). The new parametrization depends on the initial (qi) and final (qf) values of q, on the redshift of the transition from deceleration to acceleration (zt) and the width of such transition (τ). We show that although supernovae (SN) observations (Gold182 and SNLS data samples) indicate, at high confidence, that a transition occurred in the past (zt > 0) they do not, by themselves, impose strong constraints on the maximum value of zt. However, when we combine SN with the measurements of the ratio between the comoving distance to the last scattering surface and the SDSS + 2dfGRS BAO distance scale (Sk/Dv) we obtain, at 95.4% confidence level, and for (Sk/Dv+Gold182), and and for (Sk/Dv+SNLS), assuming qi = 0.5 and qf = −1. We also analyze the general case, qf  (−∞, 0) finding the constraints that the combined tests (Sk/Dv+SNLS) impose on the present value of the deceleration parameter (q0).  相似文献   

17.
The positron acoustic shock and solitary wave are explored in nonextensive electron-positron-ion plasma. The plasma system under-consideration, consists of a classical positron beam, q distributed electrons and positively charged bulky ions constitute a neutralizing background. The nonlinear Korteweg-de Vries and Burger equations are derived by employing the standard reductive perturbation method. The positron acoustic wave in linear limit is also discussed for dissipative as well as nondissipative cases of nonextensive plasmas. The plasma parameters such as, the concentration of neutralizing ions background, beam velocity, temperature and q parameter of the nonextensive electrons are noticed to significantly affect the positron acoustic shock and solitary waves. Our findings may be helpful in the understanding of laboratory beam plasma interaction experiments as well as the astrophysical nonextensive plasmas interacting with positron beam.  相似文献   

18.
The Friedmann universes are built on the cosmological principle only. The Robertson-Walker metric is common to all the theories based on a homogeneous, isotropic and irrotational universe. In the present work we examine ways of constructing a metric conformal with that of Robertson and Walker, by means of a variational principle which takes into account the cosmological principle as stated by Weinberg (1972), and based on the existence of orbits generated by a one-parameter group of diffeomorphisms of physical space. The application of the cosmological principle to variational methods allows the determination of first integrals which can characterize the physical properties of the Universe. To this end, we show that the Lagrangian of the Universe, considered as a mechanical system, can be chosen from the germs of functions, and that the form variations δq i are tangent vectors of the group orbits in a Riemannian manifold. Thus the variation of the action vanishes automatically. There appears a first integral of the Euler equations, which is δq i (?L/?q1 i ) = C te , and also the condition ?L/?t=0, which means the uniformity of time in a Lagrangian conservative system, and which is a direct application of the cosmological principle. These conditions allow the effective determination of a form invariant Lagrangian in the case of isometries. These conditions can be generalized to the case in which the group trajectories are a partition of physical space. Thus, it is possible to define a time from the group trajectories inV 3: a second of the group time is a lengthm measured along any orbit θ p of the group. Any pointp of the manifold can then be considered as the starting point of a bundle of orbits, along which the tangent vectors δq i could be calculated. From this group time, we can build a metric ds 2 conformal to the initial ds 2 and for which the orbits, which are geodesic, are orthogonal to the transitivity surfaces of the group in the manifold. This implies new statements of the cosmological principle:
  1. At any point of space-time it is possible to construct a metric ds 2 from the trajectories generated by a one-parameter group of diffeomorphisms ofV 4.
  2. Any two points of space-time can always be joined by means of trajectories of group.
The variational implications of these two principles are the appearance of spectral line shifts such as 1+z=F(p, t p)/F(q, tq), wherep andq are arbitrary points of the manifold, andF the transformation function which allows passage from one metric to another. The identification of group trajectories with physical trajectories depends on these two principles. The photon trajectories inV 3 is an example of this identification. The trajectories of charged particles inV 4 are another. Principle (b) stated an entropy condition; its application allows a new expression of action variation, this one leading to a general formulation of the shift of spectral lines by a variational method. If we choose the parabolic Friedmann universe as a realistic model, it is the expansion itself which is the generator of the diffeomorphisms allowing the establishment of a group structure in the manifold. The photons are carried away by expansion and do not resist it. The massive particles moderate this expansion locally, and their trajectories inV 3 are the result of the reaction. In this scheme there is no theoretical difference between the treatment of particles of vanishing proper mass and massive particles. The Robertson-Walker metric fork=0 corresponds to a picture of the Universe which can be drawn by study of the movement of photons in physical space. Only the study of particles can allow the generalization of this scheme and, from this, make a real Universe which is not just a reflection of the physical properties of the photons alone.  相似文献   

19.
The dust-acoustic shock waves have been theoretically investigated using reductive perturbation technique. An unmagnetized four-component dusty plasma system consisting of nonextensive q-distributed electrons, Boltzmann distributed ions, and negatively as well as positively charged dust particles has been considered. The solution of Burgers equation in planar geometry is numerically analyzed. It has been observed that the nonextensive q-distribution of electrons has a significant role in the formation of shock waves. The relevance of our results to astrophysics as well as laboratory plasmas are briefly discussed.  相似文献   

20.
Stimulated by the recent debate on the physical relevance and on the predictivity of q-Gaussian formalism, we present specific analytical expressions for the parameters characterizing non-Gaussian distributions, such as the nonextensive parameter q, expressions that we have proposed for different physical systems, an important example being plasmas in the stellar cores.  相似文献   

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