The stationary state and gravitational temperature in a pure self-gravitating system

Zheng, Yong; Du, Jiulin

doi:10.1016/j.physa.2014.10.086

Cited by 11 publications

(14 citation statements)

References 26 publications

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“…which now is familiar to us in Refs. [5,[39][40][41]. Now let us evaluate the values of these two types of nonextensive parameters in Eq.(107).…”

Section: The Single-particle Q-distribution In the Canonical Ensemblementioning

confidence: 99%

“…This is equal to say, the quantum statistics is approximately irrelevant to the physical processes or phenomena where the position and size of particles are important. On the contrary, the nonexetnsive effect is relevant to the position of particles, such as the systems including long-range interactions and correlations [5,40,41], or the sizes of particles, such as the sizes of molecules or the Van der Waals radii [46]. About the second case, let us make more interpretation.…”

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confidence: 99%

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The nonextensive statistical ensembles with dual thermodynamic interpretations

Zheng

Liu

et al. 2019

Eur. Phys. J. Plus

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The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for the limit of large particle number for most normal systems. In this case, Tsallis entropy can be expanded as a function of energy and particle number fluctuation, and thus the power-law forms of the generalized Gibbs distribution and grand canonical distribution can be derived. These new distribution functions can be applied to derive the free energy and grand thermodynamic potential in nonextensive thermodynamics. In order to establish appropriate nonextensive thermodynamic formalism, the dual thermodynamic interpretations are necessary for thermodynamic relations and thermodynamic quantities. By using a new technique of parameter transformation, the single-particle distribution can be deduced from the power-law Gibbs distribution. This technique produces a link between the statistical ensemble and the quasi-independent system with two kinds of nonextensive parameter having quite different physical explanations. Furthermore, the technique is used to construct nonextensive quantum statistics and effectively to avoid the factorization difficulty in the power-law grand canonical distribution.

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“…which now is familiar to us in Refs. [5,[39][40][41]. Now let us evaluate the values of these two types of nonextensive parameters in Eq.(107).…”

Section: The Single-particle Q-distribution In the Canonical Ensemblementioning

confidence: 99%

mentioning

confidence: 99%

The nonextensive statistical ensembles with dual thermodynamic interpretations

Zheng

Liu

et al. 2019

Eur. Phys. J. Plus

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“…Eq. (2) has been applied to test the nonextensivity in the helioseismological measurements of the Sun [44], to constitute the astrophysical convection instability criterion [45,46], to analyze the thermodynamic stability of self-gravitating system [47], and to introduce the concept of the gravitational heat conduction [48] and the gravitational temperature [49]. Eq.…”

Section: -----------------------------------------mentioning

confidence: 99%

The nonextensive parameter for the rotating astrophysical systems with power-law distributions

2016

EPL

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We study the nonextensive parameter for the rotating astrophysical systems with power-law distributions, including both the rotating self-gravitating system and the rotating space plasma. We extend the equation of nonextensive parameter to complex system with arbitrary force field F(r,v)=F (r)+α v×F (r), 1 2 and derive a general equation of the q-parameter, most generally including both the rotating self-gravitating systems and the rotating space plasmas. At the same time, we reproduce the κ-distribution in space plasmas and obtain equations of the κ-parameter.We show that the q-parameter is related not only to the temperature gradient, the gravitational force and the electromagnetic force, but also to the inertial centrifugal force and Coriolis force. Thus the rotation introduces significant effect on nonextensivity in the systems. Several examples are given to illustrate the nonextensive effect introduced by the rotation.

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“…Therefore, the key to fill in the gaps in the astrophysical thermodynamics is to present one feasible idea about the temperature definition. Perhaps it can be done through the assumption of temperature duality [10], according to which the gravitational temperature can de defined in the astrophysical systems [11]. With the gravitational temperature, the heat conduction driven by the gravity can be naturally discovered.…”

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confidence: 99%

“…So the gravitational temperature reveals the kinetic energies and potential energies of the particles consisting of the self-gravitating system. That is why the gravitational thermal capacity defined dependent on the generalized temperature is possible to be positive [11].…”

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confidence: 99%

The gravitational heat conduction and the hierarchical structure in solar interior

Zheng¹,

Du²

2014

EPL

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With the assumption of local Tsallis equilibrium, the newly defined gravitational temperature is calculated in the solar interior, whose distribution curve can be divided into three parts, the solar core region, radiation region and convection region, in excellent agreement with the solar hierarchical structure. By generalizing the Fourier's law, one new mechanism of heat conduction, based on the gradient of the gravitational temperature, is introduced into the astrophysical system. This mechanism is related to the self-gravity of such self-gravitating system whose characteristic scale is large enough. It perhaps plays an important role in the astrophysical system which, in the solar interior, leads to the heat accumulation at the bottom of the convection layer and then motivates the convection motion.Keywords: Gravitational temperature; heat conduction; convection motion. PACS: 44.10.+i; 51.20.+d; 96.60.Jw.As everyone knows, almost all the physical systems treated in statistical mechanics with the Boltzmann-Gibbs (BG) entropy are extensive and this property holds for the systems with short-range interactions. However, when dealing with the systems with long-range interactions such as Newtonian gravitational forces and Coulomb electric forces, the BG statistics may need to be generalized for their statistical description.In recent years, nonextensive statistics mechanics (NSM) based on Tsallis entropy [1] has been proposed as a generalization of BG statistics. This new statistics theory has been used to deal with many interesting problems in the systems with long-range interactions, among which the self-gravitating system is one important research field [2-6]. The theoretic and observational successes for the NSM in this field show that, possibly this statistics theory is one fundamentally valid method to describe the astrophysical system. Combining the Newtonian mechanics or general relativity, it can be used to interpret various phenomena in astrophysics.On the other hand, it is difficult for the scientists to carry out the thermodynamic research on the astrophysical system. The ordinary results they could obtain in their researches are the gravothermal catastrophe [7,8] and the negative thermal capacity [7]. These results prevent people from getting more insight into the essence of the gravity in the view of thermodynamics. Although with the NSM these results can be avoided partly [9], it is very difficult to formally introduce the heat conduction mechanism, in the astrophysical sense, into the self-gravitating system. The main reason for this is that, in the development process of the NSM, the controversy on the temperature definition holds back the emergence of the thermodynamics in the framework of the NSM.

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The stationary state and gravitational temperature in a pure self-gravitating system

Cited by 11 publications

References 26 publications

The nonextensive statistical ensembles with dual thermodynamic interpretations

The nonextensive statistical ensembles with dual thermodynamic interpretations

The nonextensive parameter for the rotating astrophysical systems with power-law distributions

The gravitational heat conduction and the hierarchical structure in solar interior

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