Nonextensive thermodynamic relations

Abe, Sumiyoshi; Martı́nez, S.; Pennini, F.; Plastino, A.

doi:10.1016/s0375-9601(01)00127-x

Cited by 226 publications

(226 citation statements)

References 11 publications

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“…But the average value will lose the distribution information about the inhomogeneous nature, and is unable to determine or mark the state of this system. Fortunately, we have confirmed that, for the nonextensive system like the self-gravitating one, the concept of temperature could generally split into two: the physical temperature related to the nonextensivity of the whole system [19], and the Lagrange temperature (the inverse of Lagrange multiplier) related to the local molecular collisions. The former is used to describe the 'equilibrium' state of the nonextensive system, and the latter is the measurable quantity in experiments.…”

Section: The Gravitational Temperaturementioning

confidence: 69%

“…One can find the condition (21) is satisfied naturally at the 'equilibrium' state. This expression is different from the physical temperature defined from the ensemble theory [19,20]. The gravitational temperature defined here is the molecular kinetics form of the physical temperature in the pure self-gravitational system and therefore is identical to physical temperature.…”

Section: The Gravitational Temperaturementioning

confidence: 93%

“…This is just the assumption of temperature duality [20]. In a pure self-gravitating system, we also employ this temperature assumption, and similar to the definition of physical temperature in the ensemble theory [19] one can introduce a new concept of the generalized temperature for the molecular dynamics.…”

Section: The Gravitational Temperaturementioning

confidence: 99%

“…Furthermore, the relation between the gravitational temperature (i.e. the physical temperature in nonextensive statistics [19,20]) and the Lagrange temperature is…”

Section: The Tsc and The Gravitational Thermal Capacitymentioning

confidence: 99%

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

Zheng

2015

Physica A: Statistical Mechanics and its Applications

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The pure self-gravitating system in this paper refers to a multi-body gaseous system where the self-gravity plays a dominant role and the intermolecular interactions can be neglected. Therefore its total mass must be much more than a limit mass, the minimum mass of the system exhibiting long-range nature. Thee method to estimate the limit mass is then proposed. The nonequlibrium stationary state in the system is identical to the Tsallis equilibrium state, at which the Tsallis entropy approaches to its maximum. On basis of this idea, we introduce a new concept of the temperature whose expression includes the gravitational potential and therefore we call it gravitational temperature. Accordingly, the gravitational thermal capacity is also introduced and it can be used to verify the thermodynamic stability of the astrophysical systems.

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Section: The Gravitational Temperaturementioning

confidence: 69%

Section: The Gravitational Temperaturementioning

confidence: 93%

Section: The Gravitational Temperaturementioning

confidence: 99%

“…Furthermore, the relation between the gravitational temperature (i.e. the physical temperature in nonextensive statistics [19,20]) and the Lagrange temperature is…”

Section: The Tsc and The Gravitational Thermal Capacitymentioning

confidence: 99%

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

Zheng

2015

Physica A: Statistical Mechanics and its Applications

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“…Raggio [10] had already shown that the equivalence between the first and third versions of Tsallis' formalism by utilizing the "q ↔ 1/q"-duality, i.e., maximizing S q under the energy constraint of U (3) q is equivalent to maximizing S 1/q under that of U (1) . Through the efforts [11,12] to generalize the zeroth law of thermodynamics within Tsallis' thermostatistics, it was revealed that the inverse temperature is not simply the Lagrange multiplier associated with the energy constraint. For this reason, the Tsallis variational problem and the Legendre transform structures have been extensively studied by e.g., so-called optimal Lagrange multiplier (OLM) formalism [13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy

Wada

Scarfone

2005

Physics Letters A

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Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy Abstract Tsallis' thermostatistics with the standard linear average energy is revisited by employing S 2−q , which is the Tsallis entropy with q replaced by 2 − q. We explore the connections among the S 2−q approach and the other different versions of Tsallis formalisms. It is shown that the normalized q-average energy and the standard linear average energy are related to each other. The relations among the Lagrange multipliers of the different versions are revealed. The relevant Legendre transform structures concerning the Lagrange multipliers associated with the normalization of probability are studied. It is shown that the generalized Massieu potential associated with S 2−q and the linear average energy is related to one associated with the normalized Tsallis entropy and the normalized q-average energy.

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Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Farhadkiyaei

Dorranian

2017

Contrib. Plasma Phys

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Effects of plasma nonextensivity on the nonlinear cnoidal ion-acoustic wave in unmagnetized electron-positron-ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion-acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron ( ). For all of the acceptable values of q, the cnoidal ion-acoustic wave is compressive. Results show that ion-acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and on the characteristics of the ion-acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency. KEYWORDScnoidal wave, electron-positron-ion plasma, ion-acoustic nonlinear wave, plasma nonextensivity, solitary wave INTRODUCTIONPlasma is mainly the science of universe, new accelerators, and new source of energy. Furthermore, there are many other applications of plasma that is penetrating into the technology of our ordinary life. [1,2] Plasma is a multimode medium. Depending on plasma species and condition, as well as plasma energy, a wide range of longitudinal or transverse modes in cnoidal or soliton form may generate in plasma medium. Some of them may be observed in linear regime, but there are a large number of plasma modes that will appear after taking the nonlinearity into account. Because of its high energy, the nonlinear phenomena play an essential role in plasma medium.Normal plasmas comprise of electrons, ions, and neutral particles. In the case of high-energy plasma, positrons will be produced in the medium due to pair production phenomena. The electron-positron-ion (e-p-i) plasma has an important role in the understanding of the plasmas in the early universe, [3,4] in active galactic nuclei, [5] in pulsar magnetospheres, [6,7] and in the solar atmosphere.[8] It is well known that when positrons are introduced into e-i plasma, the response of the plasma changes significantly. The presence of positrons has some application in plasma. For instance, they can be used to probe particle transport in tokamaks, and since they have sufficient lifetime, the two-component (e-i) plasma becomes three-component (e-p-i) plasma. [9][10][11][12][13] Most of the astrophysical plasmas also contain positrons in addition to electrons and ions. During the last decade, e-p-i plasma has attracted the attention of several authors. They have studied the linear and nonlinear wave propagation in e-p-i plasmas using different models. [14][1...

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Nonextensive thermodynamic relations

Cited by 226 publications

References 11 publications

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

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

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized q-average energy

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

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