Temperature and pressure in nonextensive thermostatistics

Wang, Q. A.; Nivanen, Laurent; Méhauté, Alain Le; Pezeril, M.

doi:10.1209/epl/i2003-10171-6

Cited by 37 publications

(53 citation statements)

References 22 publications

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“…The definition of the physical temperature in the nonextensive statistics is still an open issue [25,26,27,28,29,30,31,32,33]. From a pragmatic point of view, since (β ′ q ) −1 has the dimension of energy, (β ′ q k) −1 is a temperature scale which can be used to interpret experimental results.…”

Section: Nonextensive Statistics and Monte Carlo Simulationmentioning

confidence: 99%

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Crokidakis¹,

Soares-Pinto²,

Reis³

et al. 2009

Phys. Rev. E

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In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic 2D Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for q ≤ 0.5. However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the 0.5 < q ≤ 1.0 regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents α, β and γ depend on the entropic index q in the range 0.5 < q ≤ 1.0 in the form α(q) = (10 q 2 − 33 q + 23)/20, β(q) = (2 q − 1)/8 and γ(q) = (q 2 − q + 7)/4. On the other hand, the critical exponent ν does not depend on q. This suggests a violation of the scaling relations 2 β + γ = d ν and α + 2 β + γ = 2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.

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Section: Nonextensive Statistics and Monte Carlo Simulationmentioning

confidence: 99%

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Crokidakis¹,

Soares-Pinto²,

Reis³

et al. 2009

Phys. Rev. E

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“…Physical mechanisms responsible for the successful application of the nonextensive statistical approach to the description of the particle spectra in this systems is a topic of discussion [31][32][33][34][35][36]. However, the analysis presented in this paper uses the Tsallis formalism primarily as a parameterization to describe the particle spectra and compares it with other parameterizations used for the spectra approximation.…”

mentioning

confidence: 99%

Measurement of neutral mesons inp+pcollisions ats=200 GeVand scaling properties of hadron production

Adare¹,

Afanasiev²,

Aidala³

et al. 2011

Phys. Rev. D

206

107

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The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the invariant differential cross section for production of K 0 S , ω, η ′ , and φ mesons in p + p collisions at √ s = 200 GeV. Measurements of ω and φ production in different decay channels give consistent results. New results for the ω are in agreement with previously published data and extend the measured pT coverage. The spectral shapes of all hadron transverse momentum distributions measured by PHENIX are well described by a Tsallis distribution functional form with only two parameters, n and T , determining the high-pT and characterizing the low-pT regions of the spectra, respectively. The values of these parameters are very similar for all analyzed meson spectra, but with a lower parameter T extracted for protons. The integrated invariant cross sections calculated from the fitted distributions are found to be consistent with existing measurements and with statistical model predictions.

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“…This relationship is frequently considered in the development of statistical physics for nonextensive systems [5][6][7][8]. Ou et al used eq.…”

Section: We Investigate the Energy Nonadditivity Relationship E(ab) mentioning

confidence: 99%

“… characterizes the energy nonadditivity of the system under consideration and should be constant for a given system in a given situation with constant E(AB). The same logic can be found in [4] for a similar nonadditivity in entropy with many examples of empirically determined  for entropy.This relationship is frequently considered in the development of statistical physics for nonextensive systems [5][6][7][8]. Ou et al used eq.…”

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confidence: 99%

Investigation of an energy nonadditivity for nonextensive systems

Djanteng

Kaabouchi

et al. 2011

Chin. Sci. Bull.

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We investigate the energy nonadditivity relationship E(AB) = E(A) + E(B) + E(A)E(B)which is often considered in the development of the statistical physics of nonextensive systems. It was recently found that  in this equation was not constant for a given system in a given situation and could not characterize nonextensivity for that system. In this work, we select several typical nonextensive systems and compute the behavior of  when a system changes its size or is divided into subsystems in different fashions. Three kinds of interactions are considered. It is found by a thought experiment that  depends on the system size and the interaction as expected and on the way we divide the system. However, one of the major results of this work is that, for given system,  has a minimum with respect to division position. Around this position, there is a zone in which  is more or less constant, a situation where the sizes of the subsystems are comparable. The width of this zone depends on the interaction and on the system size. We conclude that if  is considered approximately constant in this zone, the two mathematical difficulties raised in previous studies are solved, meaning that the nonadditive relationship can characterize the nonadditivity of the system as an approximation. In all the cases,  tends to zero in the thermodynamic limit (N→) as expected. Many kinds of physical systems in nature are recognized as energy nonadditive or nonextensive 1) . This includes small size systems as well as large size systems having long range interaction such as gravity. For these systems, knowing the nonadditivity or nonextensivity in energy and entropy will be very useful for understanding some physical properties and for establishing corresponding theoretical descriptions. Energy and entropy additivity is a crucial hypothesis and a cornerstone for many physical theories [1]. How to replace this basic hypothesis is obviously a puzzling problem. In view of the diversity of the nonadditive systems in nature [2,3], it is unlikely that a universally valid and simple relationship exists.In this work, we focus on a special relationship of energy nonadditivity given bywhere A and B are two subsystems of a composite system AB and E is their energy.  characterizes the energy nonadditivity of the system under consideration and should be constant for a given system in a given situation with constant E(AB). The same logic can be found in [4] for a similar nonadditivity in entropy with many examples of empirically determined  for entropy.This relationship is frequently considered in the development of statistical physics for nonextensive systems [5][6][7][8]. Ou et al. used eq. (1) as a first principle to show that the q-exponential distribution [8] can occur in small systems

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Temperature and pressure in nonextensive thermostatistics

Cited by 37 publications

References 22 publications

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Measurement of neutral mesons inp+pcollisions ats=200 GeVand scaling properties of hadron production

Investigation of an energy nonadditivity for nonextensive systems

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