Quantum Statistical Mechanics for Nonextensive Systems: Prediction for Possible Experimental Tests

Rajagopal, A. K.; Mendes, R. S.; Lenzi, E. K.

doi:10.1103/physrevlett.80.3907

Cited by 77 publications

(91 citation statements)

References 23 publications

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“…In this way, employing Eqs. (18) and (19) with the Hamiltonian given by (2) and taking into account Eq. (11), we obtain that…”

Section: Iii-exact Versus Approximate Calculations and Normalized Conmentioning

confidence: 99%

“…These investigations are basically employed in the discussion of aspects related to nonextensive phenomena, such as, Lévy-type anomalous superdiffusion [5], Euler turbulence [6], self-gravitating systems and related themes [6,7,8,9,10], cosmic background radiation [11,12,13,14], peculiar velocities in galaxies [15], eletron-phonon interaction [16], and ferrofluid-like systems [17]. In addition, some important methods of the usual Boltzmann-Gibbs statistics have been generalized in order to incorporate the Tsallis framework, e. g., linear response theory [18], Green function theory [19] and path integral [20]. However, exact calculations are generally difficult to be performed in the context of Tsallis statistics.…”

Section: I-introductionmentioning

confidence: 99%

See 1 more Smart Citation

Remarks on (1−q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

Lenzi¹,

Mendes²,

Silva³

et al. 2001

Physics Letters A

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The validity of (1-q) expansion and factorization approximations are analysed in the framework of Tsallis statistics. We employ exact expressions for classical independent systems (harmonic oscillators) by considering the unnormalized and normalized constrainsts. We show that these approxiamtions can not be accurate in the analysis of systems with many degrees of freedom. I-IntroductionEver since the presentation by Tsallis[1, 2, 3] of a new possible generalization of the statistical mechanics (Tsallis statistics) based on the nonextensive entropy,a large number of investigations has been developed concerning this subject [4]. These investigations are basically employed in the discussion of aspects related to nonextensive phenomena, such as, Lévy-type anomalous superdiffusion [5], Euler turbulence[6], self-gravitating systems and related themes [6,7,8,9,10], cosmic background radiation [11,12,13,14] [11,13,14] and in other many independent particle systems [27,28,29,30,31,32], but without a careful analysis of the validity of these methods. Thus, a detailed discussion of the (1 − q) expansion and the factorization approximation plays a special role in this scenario. In this direction, Ref.[33] contains a discussion comparing these approximations in the context of the quantum gases. However, some important aspects of the comparison are still lacking, in particular the importance of the degrees of freedom N . This work is addressed to analyze how precise the (1−q) expansion and the factorization approximation are by considering N arbitrary. To perform this study it is convenient to consider a solvable model in order to carefully understand the degree of accuracy of these approximations. Furthermore, the chosen model must contain important features of other more realistic ones. This is just the case of a set of harmonic oscillators.In this direction, to analyze the (1 − q) expansion and the factorization approximation, we focus our discussion on the classical Tsallis statistics by considering N one dimesional harmonic oscillators, i. e., we employ the Hamiltonian H =

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“…In this way, employing Eqs. (18) and (19) with the Hamiltonian given by (2) and taking into account Eq. (11), we obtain that…”

Section: Iii-exact Versus Approximate Calculations and Normalized Conmentioning

confidence: 99%

Section: I-introductionmentioning

confidence: 99%

Remarks on (1−q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

Lenzi¹,

Mendes²,

Silva³

et al. 2001

Physics Letters A

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“…Alternatively, it can be obtained maximizing Tsallis entropy under the constraints imposed by normalization and the energy mean value [10], a procedure closely related to Jaynes information theory formulation of statistical mechanics [11,12]. So far, most theoretical studies on Tsallis thermostatistics have been developed on the basis of the maximum entropy principle [1,13,14,15]. As widely known, this approach to statistical ensembles was, in the case of standard statistical mechanics, historically the latest one to appear.…”

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confidence: 99%

Nonextensive Thermostatistics and theHTheorem

2001

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The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis". For q > 0, the q-transport equation satisfies an H-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.PACS numbers: 05.45.+b; 05.20.-y; 05.90.+m In 1988 Tsallis proposed a striking generalization of the Boltzmann-Gibbs entropy functional given by [1],

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“…This result shows that the above Green function satisfies the same periodic boundary condition of the usual one [13], in contrast to the one [14] formulated within the Tsallis formalism [15]. Similar to what is done in the usual case, we may introduce the spectral function, A(p,ω), defined as A(p,ω) = G > (p, ω)∓G < (p, ω) and express G < and G > as follows:…”

Section: Nonlocal Effects and Green Functionmentioning

confidence: 78%

Nonlocal effects on the thermal behavior of non-crystalline solids

Lenzi¹,

Astrath

Rossato³

et al. 2009

Braz. J. Phys.

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We argue that nonlocal effects represented by fractionary terms in the kinetic energy can be relevant to achieve a satisfactory phenomenological description of the thermal behavior of the specific heat of non-crystalline solids at very low temperature. We propose a simple model formed by the direct sum of two Hamiltonians, one of which is obtained by incorporating fractional derivatives in the kinetic energy of a conventional Hamiltonian, and the other one accounts for the presence of phonons in the system. Some experimental data are used to support the proposed description.

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Quantum Statistical Mechanics for Nonextensive Systems: Prediction for Possible Experimental Tests

Cited by 77 publications

References 23 publications

Remarks on (1−q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

Remarks on (1−q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

Nonextensive Thermostatistics and theHTheorem

Nonlocal effects on the thermal behavior of non-crystalline solids

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