Jiulin Du

Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactions

Abstract The nonextensivity in a nonisothermal plasma system with the Coulombian long-range interaction is studied in the framework of Tsallis statistics. We present for first time a mathematical expression of the nonextensive parameter q based on the mathematical theory about the generalized Boltzmann equation and the q–H theorem and the Maxwellian q-velocity distribution. We obtain a new physical explanation for q ≠ 1 related to the nature of nonisothermal configurations in the plasma systems with the Coulombian long-range interaction, which means that Tsallis statistics might be a suitable statistics for the description of a nonequilibrium system with long-range interactions and with a temperature gradient in it.

A nonextensive approach for the instability of current-driven ion-acoustic waves in space plasmas

The instability of current-driven ion-acoustic waves in the collisionless magnetic-field-free space plasma is investigated by using a nonextensive approach. The ions and the electrons are thought of in the power-law distributions that can be described by the generalized q-Maxwellian velocity distribution and are considered with the different nonextensive q-parameters. The generalized q-wave frequency and the generalized instability q-growth rate for the ion-acoustic waves are derived. The numerical results show that the nonextensive effects on the ion-acoustic waves are not apparent when the electron temperature is much more than the ion temperature, but they are salient when the electron temperature is not much more than the ion temperature. As compared to the electrons, the ions play a dominant role in the nonextensive effects.

Dust acoustic instability driven by drifting ions and electrons in the dust plasma with Lorentzian kappa distribution

The instability of the dust acoustic waves driven by drifting electrons and ions in a dusty plasma is investigated by the kinetic theory. All the plasma components (electrons, ions, and dust particles) are assumed to be the Lorentzian κ (kappa) distributions. The spectral indices κ of the κ-distributions for the three plasma components are different from each other. The obtained instability growth rate depends on the physical quantities of the plasma not only, but on the spectral indices. The numerical results for the κ-effect on the instability growth rate show that, if the normalized wave number is small, the index of electrons has a stabilized effect on the dust acoustic waves and the index of ions has an instability effect on the waves, but if the normalized wave number is large, they both nearly have no any effect on the waves. In reverse, the index of dust grains has nearly no any effect on the instability growth rate if the normalized wave number is small, but it has a stabilized effect on the dust...

Test of nonextensive statistical mechanics by solar sound speeds

To check the validity of the theory of nonextensive statistical mechanics, we have investigated the nonextensive degree of the solar interior and have tried to find the experimental evidence by helioseismological measurements that q is different from unity. We are able to derive a parameter for providing a lower limit to the nonextensive degree inside the Sun that can be uniquely determined by the solar sound speeds measured by helioseismology. After calculating the parameter by using the solar sound speeds, we get the lower limit of (1 − q) ≥ 0.1902 for all solar radii between 0.15R⊙ and 0.95R⊙ and (1 − q) ≈ 0.4 for the out layers, 0.75R⊙ ≤ r ≤ 0.95R⊙. Thus, the result that the nonextensive parameter q is significantly different from unity has received the support by the experiment measurements in helioseismology.

Transition state theory: A generalization to nonequilibrium systems with power-law distributions

Transition state theory (TST) is generalized to nonequilibrium systems with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by Langevin equations and corresponding Fokker–Planck equations. It is considered that a system far away from equilibrium does not have to relax to a thermal equilibrium state with Boltzmann–Gibbs distribution, but asymptotically approaches a nonequilibrium stationary state with a power-law distribution. Thus, we obtain a possible generalization of TST rates to nonequilibrium systems with power-law distributions. Furthermore, we derive the generalized TST rate constants for one-dimensional and n-dimensional Hamiltonian systems away from equilibrium, and obtain a generalized Arrhenius rate for systems with power-law distributions.

The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the kappa parameter and the kappa-distribution in the kappa-deformed statistics, based on Kaniadakis entropy, for a relativistic gas in an electromagnetic field. We derive two relations for the relativistic gas in the framework of kappa-deformed statistics, which describe the physical situation represented by the relativistic kappa-distribution function, provide a reasonable connection between the parameter kappa, the temperature four-gradient and the four-vector potential gradient, and thus present for the case kappa different from zero a clearly physical meaning. It is shown that such a physical situation is a meta-equilibrium state of the system, but has a new physical characteristic.

The κ parameter and κ-distribution in κ -deformed statistics for the systems in an external field

Abstract It is naturally important question for us to ask under what physical situation should the κ -deformed statistics be suitable for the statistical description of a system and what should the κ parameter stand for. In this Letter, a formula expression of κ parameter is derived on the basis of the κ – H theorem, the κ -velocity distribution and the generalized Boltzmann equation in the framework of κ -deformed statistics. We thus obtain a physical interpretation for the parameter κ ≠ 0 with regard to the temperature gradient and the external force field. We show, as the q -statistics based on Tsallis entropy, the κ -deformed statistics may also be the candidate one suitable for the statistical description of the systems in external fields when being in the nonequilibrium stationary state, but has different physical characteristics. Namely, the κ -distribution is found to describe the nonequilibrium stationary state of the system where the external force should be vertical to the temperature gradient.

Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution

The dust charging processes in the collections of electrons and ions in the nonequilibrium dusty plasma with power-law distributions are investigated on the basic of a new q-distribution function theory in nonextensive statistics. Electrons and ions obey the power-law distributions and are with q-parameters different from each other. We derive the generalized formulae for the dust charging currents in which the nonextensive effects play roles. Further we investigate the dust charging processes taking place in the homogeneous dusty plasma where only the particle velocities are power-law distributions and in the dust cloud plasma where the particle velocities and densities are both power-law distributions. By numerical analyses, we show that the nonextensive power-law distributions of electrons and ions have significant effects on the dust charging processes in the nonequilibrium dusty plasma.

Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations

We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker–Planck equation, we can obtain a condition under which these power-law distributions are accurately created in a system away from equilibrium. This condition is an energy-dependent relation between the diffusion coefficient and the friction coefficient and thus it provides a fluctuation-dissipation relation for nonequilibrium systems with power-law distributions. Further, we study the specific forms of the Fokker–Planck equation that correctly lead to such power-law distributions, and then present a possible generalization of the Klein–Kramers equation and the Smoluchowski equation to a complex system, whose stationary-state solutions are exactly a Tsallis distribution.

The power-law reaction rate coefficient for an elementary bimolecular reaction

The power-law TST reaction rate coefficient for an elementary bimolecular reaction is studied when the reaction takes place in a nonequilibrium system with power-law distributions. We derive a generalized TST rate coefficient, which not only depends on a power-law parameter but also on the reaction coordinate frequency of transition state. The numerical analyses show a very strong dependence of the TST rate coefficient on the power-law parameter, and clearly indicate that a tiny deviation from unity in the parameter (thus from a Boltzmann–Gibbs distribution) would result in significant changes in the rate coefficient. We take an elementary reaction, F+H2→FH+H, as an application example to calculate the reaction rate coefficient, and yield the rate values being exactly in agreement with the measurement values in all the experimental studies in the temperature range 190–765 K.