Nonextensive Thermostatistics and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">H</mml:mi></mml:math>Theorem

Lima, J. A. S.; Silva, R.; Plastino, A.

doi:10.1103/physrevlett.86.2938

Cited by 201 publications

(238 citation statements)

References 28 publications

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“…The distribution function f ( ) in this equation satisfies the generalized Boltzmann equation in the nonextensive statistical framework [17],…”

Section: The Nonequilibrium Stationary State and Tsallis Equilibriummentioning

confidence: 99%

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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“…The distribution function f ( ) in this equation satisfies the generalized Boltzmann equation in the nonextensive statistical framework [17],…”

Section: The Nonequilibrium Stationary State and Tsallis Equilibriummentioning

confidence: 99%

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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“…(16). Let us note that a similar expression for the function h q was previously introduced in Ref.s [10] and a rigorous justification of the validity of the ansatz (53) can be found only by means of a microscopic analysis of the dynamics of correlations in nonextensive statistics.…”

Section: Nonextensive Relativistic Dynamicsmentioning

confidence: 99%

“…This matter of fact is a direct consequence of the nonextensive statistical prescription of the normalized q-mean expectation value and is not taken into account in the non-relativistic formulation of Ref. [10].…”

Section: Nonextensive Relativistic Dynamicsmentioning

confidence: 99%

Generalized classical and quantum dynamics within a nonextensive approach

Lavagno¹

2005

Braz. J. Phys.

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On the basis of generalized classical kinetic equations, reproducing the stationary distribution of the Tsallis nonextensive thermostatistics, we formulate two generalized Schrödinger equations which satisfy the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. Moreover, we study the generalization of the previously introduced dynamic equations in a relativistic regime and we apply our results to the study of the rapidity distribution in the relativistic heavy-ion collisions.

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“…Recently, Lima et al [2] (see also [3]) advanced an ad-hoc modification of the Stosszahlansatz, in order to derive a proof of the H-theorem, and to obtain the corresponding collisional equilibrium velocity distribution, within the framework of Tsallis' nonextensive thermostatistics [4]. In this paper, we show that there is no need of modifying the functional form of the molecular chaos hypothesis for accomplishing this task.…”

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confidence: 98%

“…The quantity R q (f, f ′ ) is a difference of two correlation functions (just before and after collision). At this point we depart from [2], who originally proposed that…”

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confidence: 99%

Nonextensive thermostatistics and the H-theorem revisited

Ramos

Rosa

Bambace

2004

Physica A: Statistical Mechanics and its Applications

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In this paper we present a new derivation of the H-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we do not assume any modification on the functional form of Boltzmann's original "molecular chaos hypothesis". Rather, we explicitly introduce into the collision scenario, the existence of statistical dependence between the molecules before the collision has taken place, through a conditional distribution f ( v 2 | v 1 ). In this approach, different equilibrium scenarios emerge depending on the value of the nonextensive entropic parameter.

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Nonextensive Thermostatistics and theHTheorem

Cited by 201 publications

References 28 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

Generalized classical and quantum dynamics within a nonextensive approach

Nonextensive thermostatistics and the H-theorem revisited

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