Nonextensive thermostatistics and the H-theorem revisited

Ramos, Fernando M.; Rosa, Reinaldo R.; Bambace, L. A. W.

doi:10.1016/j.physa.2004.06.042

Cited by 10 publications

(11 citation statements)

References 7 publications

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“…Concentration parametrization (7) has been successfully applied to describe the dynamics of nonextensive ion [55] and electron [56] acoustic solitons. Very recently, we have found that ( 7) is fully consistent with a variational principle, leading to a critical scaling of the electrostatic potential, applying not just to nonextensive, but also Kappa, and even Thomas-Fermi acoustic soliton dynamics [57].…”

Section: Nonadiabatic Regimementioning

confidence: 99%

“…In the next section, we find a generalized polytropic index with basis on the Tsallis distribution, as given by (7).…”

Section: Nonadiabatic Regimementioning

confidence: 99%

“…Another approach, not modifying the original Boltzmann ansatz, but explicitly introducing the existence of a statistical dependence between the molecules before collisions, induces the emergence of different equilibrium scenarios, depending on the value of the nonextensive parameter [7]. Nonextensive effects on the H -theorem have been pursued even in the framework of quantum mechanics, thereby implying stationary states may be described by q-power law generalizations of Fermi-Dirac and Bose-Einstein distributions for 0 ≤ q ≤ 2 [8].…”

Section: Introductionmentioning

confidence: 99%

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Towards a physical interpretation of the deformation parametrization in nonextensive statistics

Silveira

Benetti

2021

Eur. Phys. J. Plus

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We explore new ways to interpret the role played by the deformation q-parameter in nonextensive statistics. A generalized polytropic γ -index is deduced with basis on the Tsallis distribution. In the limit q → 1/3, it is shown that the γ -index decreases hyperbolically with the increase of the concentration n of charged particles in a nonextensive gas. An equation of state of a nonextensive system is derived following the generalized polytropic index. In the limit q → 1/3, it is found that a constant and uniform isotropic pressure develops throughout a nonextensive gas of charged particles in the absence of electric and magnetic fields, and in a stationary state of equilibrium of the system. The usual reduction of the Tsallis to Kappa distributions is examined with basis on their corresponding equations of state. It is shown that such a procedure leads to a general proof of the relationship between the qparameter and spectral κ-index, and between the T -Maxwellian and -Kappa temperatures. A generalization of the number of degrees of freedom in a nonextensive gas is provided. It is suggested that a nonextensive polytropic process might characterize a system that shall be something between a monoatomic gas with more than three translational degrees of freedom, and a diatomic gas with less than three translational plus two rotational degrees of freedom. Moreover, it is proved that the restriction of the Tsallis to Kappa distributions requires that the bulk concentration n in a nonextensive gas does not exceed 50% of the concentration n 0 on its boundary, thereby characterizing a low-density system.

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Section: Nonadiabatic Regimementioning

confidence: 99%

“…In the next section, we find a generalized polytropic index with basis on the Tsallis distribution, as given by (7).…”

Section: Nonadiabatic Regimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards a physical interpretation of the deformation parametrization in nonextensive statistics

Silveira

Benetti

2021

Eur. Phys. J. Plus

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“…These distributions were largely discussed in Chateau and Meyer-Vernet (1991) and Zouganelis (2008), and citations therein. As pointed out by Valentini and D'Agosta (2007), the interest of kappa distributions to describe experimental data increased since these distributions turned out to be a consequence of entropy generalization through the generalized Boltzmann H theorem (Silva et al 1998;Lima et al 2001;Leubner 2002;Plastino et al 2004;Ramos et al 2004) in the debated non-extensive thermodynamics proposed by Tsallis (1988). Furthermore, related distribution functions are reproduced from the Fokker-Planck equation as a consequence of wave-particle interactions in the presence of collisions and are compatible with the Kullback relative entropy (Shizgal 2007).…”

Section: Introductionmentioning

confidence: 99%

Effect of superthermal electrons on dust-acoustic shock waves in coupled dusty plasmas

Pakzad

Tribeche²

2012

J. Plasma Phys.

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Nonlinear dust-acoustic (DA) shock waves in coupled dusty plasmas with negative dust grains and kappa-distributed electrons are discussed. Using a generalized hydrodynamic model, the dispersion relation and the Korteweg–de Vries-Burger (KdVB) equation for low-frequency DA modes in a strongly coupled dusty plasma are derived. The dependence of shock waves on various plasma parameters is then explored. A solitonic profile may be converted into a shock structure when correlation among dust particles becomes stronger. The amplitude as well as the steepness of shock waves increases with increasing the value of the spectral index k.

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“…Recent applications of the nonextensive entropy to an increasing number of physical problems is beginning to provide a more definite picture on the kind of scenarios where the new formalism proves to be extremely useful [3][4][5][6][7][8][9][10][11][12][13].…”

mentioning

confidence: 99%

Relativity, nonextensivity, and extended power law distributions

Silva

Lima

2005

Phys. Rev. E

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A proof of the relativistic H-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the q-parameter lies on the interval [0,2]. It is also proved that the collisional equilibrium states (null entropy source term) are described by the relativistic q-power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field F µν . Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.

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Nonextensive thermostatistics and the H-theorem revisited

Cited by 10 publications

References 7 publications

Towards a physical interpretation of the deformation parametrization in nonextensive statistics

Towards a physical interpretation of the deformation parametrization in nonextensive statistics

Effect of superthermal electrons on dust-acoustic shock waves in coupled dusty plasmas

Relativity, nonextensivity, and extended power law distributions

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