Canonical ensemble in non-extensive statistical mechanics

Ruseckas, Julius

doi:10.1016/j.physa.2015.12.011

Cited by 7 publications

(11 citation statements)

References 63 publications

(117 reference statements)

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“…We envision a "twin peaks" approach to symmetry for future work. Also, in terms of future work a treatment of this domain in terms of extended entropies would be interesting, especially given recent work [37][38][39][40][41][42][43] in connection to this field.…”

Section: Discussionmentioning

confidence: 99%

Symmetric Fractional Diffusion and Entropy Production

Prehl

Boldt

Hoffmann

et al. 2016

Entropy

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Abstract:The discovery of the entropy production paradox (Hoffmann et al., 1998) raised basic questions about the nature of irreversibility in the regime between diffusion and waves. First studied in the form of spatial movements of moments of H functions, pseudo propagation is the pre-limit propagation-like movements of skewed probability density function (PDFs) in the domain between the wave and diffusion equations that goes over to classical partial differential equation propagation of characteristics in the wave limit. Many of the strange properties that occur in this extraordinary regime were thought to be connected in some manner to this form of proto-movement. This paper eliminates pseudo propagation by employing a similar evolution equation that imposes spatial unimodal symmetry on evolving PDFs. Contrary to initial expectations, familiar peculiarities emerge despite the imposed symmetry, but they have a distinct character.

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Section: Discussionmentioning

confidence: 99%

Symmetric Fractional Diffusion and Entropy Production

Prehl

Boldt

Hoffmann

et al. 2016

Entropy

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“…The statistical mechanics of non-extensive systems is still considered an open problem [1,2]. On the one hand, many studies in the past three decades have addressed the issue of generalizations of Boltzmann-Gibbs statistical mechanics [3,4,5,6,7,8,9,10]. These studies typically assume a non-logarithmic entropy, leading to power law distributions (e.g., Zipf-Mandelbrot distributions [6,7,8]) instead of exponential distributions of energy.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The panels in the middle show log-lin plots of p(E S ) (green curve), an exponential fit (red dashed curve) over selected data (in blue), and fits with Eqs. ( 9) and (10) over the data in green for each case. The panels at the bottom of the second row show the corresponding mean bath energy E B and mean interaction energy V (red and black dashed curves with solid circles, respectively), while the bars correspond to their variance for each case.…”

Section: Intermediate-range Hamiltoniansmentioning

confidence: 99%

“…For the cases analyzed, with long-range Hamiltonians, the system is clearly non-extensive as V ≈ E B for all of the values of E S (see bottom panels in the second row), therefore, p(E S ) does not show an exponential behavior and its data are better fitted with the Eqs. ( 9) and (10) shown with the dotdash violet and dot-dash-dash orange curves respectively in (a) and (b), where we have considered a weight function that decays as an inverse power law. For the mean field case in (c), a constant fitting function was enough to describe the distribution p(E S ), shown with the dashed violet curve in the middle panel of the second row.…”

Section: Long-range Hamiltoniansmentioning

confidence: 99%

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Numerical studies for an ab initio investigation into the Boltzmann prescription in statistical mechanics of large systems

Dossetti,

Viswanathan,

Kenkre

2022

Preprint

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We present numerical investigations into the question of the validity of the Boltzmann prescription in Statistical Mechanics for large systems, addressing the issue of whether extensivity of energy implies the extensivity of the Boltzmann entropy. The importance of the question stems from the fact that it is currently considered open by some investigators but quite settled by others. We report ab initio results for gas-like Hamiltonian systems with long-range as well as short-range interactions, based on simulations that explicitly consider more than 2 30 ≈ 10 9 states of the full Hilbert space. The basis of the technique is Monte Carlo algorithms. Despite the largeness of the numbers used, careful inspection shows that the systems studied are still too small to settle uniquely the issues raised. Therefore, the new approach outlined represents a first step in addressing on first principles the question of non-extensive statistical mechanics. General theoretical comments are also supplied to supplement the numerical investigations.

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“…In nonextensive statistical ensemble theory on the complex systems, some fundamental works had been performed, for example, the generalized power-law Gibbs distributions based on the dynamical thermostatting approach [30], counting rule [31], the fractal dimension of phase space [32], and the order parameter in the generalized Lorentzian [33]. Recently, the nonextensive statistical ensemble has been restudied based on the traditional method employing the assumption of equiprobability [34,35], where the interactions between a system and its reservoir are short-range and the entropy is extensive. Therefore, more complex mechanism for the complex systems with long-range interactions has not been studied.…”

Section: Introductionmentioning

confidence: 99%

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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Canonical ensemble in non-extensive statistical mechanics

Cited by 7 publications

References 63 publications

Symmetric Fractional Diffusion and Entropy Production

Symmetric Fractional Diffusion and Entropy Production

Numerical studies for an ab initio investigation into the Boltzmann prescription in statistical mechanics of large systems

The nonextensive statistical ensembles with dual thermodynamic interpretations

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