Lectures on Nonextensive Statistical Mechanics.- I. Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status.- II. Quantum Density Matrix Description of Nonextensive Systems.- III. Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations.- IV. ComputationalMetho ds for the Simulation of Classical and Quantum Many Body Systems Arising from Nonextensive Thermostatistics.- Further Topics.- V. Correlation Induced by Nonextensivity and the Zeroth Law of Thermodynamics.- VI. Dynamic and Thermodynamic Stability of Nonextensive Systems.- VII. Generalized Simulated Annealing Algorithms Using Tsallis Statistics: Application to +-J Spin Glass Model.- VIII. Protein Folding Simulations by a Generalized-Ensemble Algorithm Based on Tsallis Statistics.

Nonextensive statistical mechanics and its applications

We investigate the dynamics of a composite system (&#x1d49e;&#x1d4ae;) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By co...

Dynamics of a composite system in a point source-induced space–time

In this comment, we discuss the mathematical formalism used in Boumali et al. (2020) which describes the superstatistical thermal properties of a one-dimensional Dirac oscillator. In particular, we point out the importance of maintaining the Legendre structure unaltered to ensure an accurate description of the thermodynamic observables when a Tsallis-like statistical description is assumed. Also, we remark that all the negative poles have to take into account to calculate the Gibbs–Boltzmann partition function. Our findings show that the divergences obtained by the authors in the Helmholtz free energy, which are propagated to the other thermal properties, are a consequence of an incomplete partition function. Moreover, we prove that the restrictions over the q -parameter are no needed if an appropriate partition function describes the system.

Comments on Superstatistical properties of the one-dimensional Dirac oscillator by Abdelmalek Boumali et al.

In this paper, we investigated the influence of energy-dependent potentials on the thermodynamic properties of the Klein-Gordon oscillator(KGO): in this way all thermal properties have been determinate via the well-know Euler-Maclaurin method. After this, we extend our study to the case of superstatistical properties of our problem in question. The probability densityf(β)followsχ2− superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated. This approximation leads to a universal parameterqfor any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameterq. Also, the influence of the this type of potentials on these properties, via the parameterγ, are well discussed.

/pdf/superstatistics-of-the-one-dimensional-klein-gordon-1bvzyk00hl.pdf

Superstatistics of the one-dimensional Klein-Gordon oscillator with energy-dependent potentials

We consider a fermion–antifermion pair interacting through Dirac oscillator interaction in one-spatial dimension and obtain an exact energy spectrum for such a composite system by solving the corresponding form of a fully covariant two-body Dirac equation. This energy spectrum shows that the considered composite system behaves as a single quantum oscillator carrying total rest mass of the particles and allows to analyze thermal properties of the system in question. To acquire this, we study the thermal properties of such a pair in the framework of the theory of superstatistics where the probability density $$f(\beta )$$
 follows three distributions: Gamma, Log-normal and F-distributions. First of all, we determine the partition function under the approximation of the low-energy asymptotics of superstatistics through the Euler–Maclaurin formula. By using the desired partition function, we determine all of the thermal properties for such a pair in terms of the parameter q and discuss the results.

Superstatistical properties of a fermion–antifermion pair interacting via Dirac oscillator coupling in one-dimension

In this paper, we consider the thermal properties of one-dimensional Dirac in the framework of the theory of superstatistics where the probability density f ( β ) follows χ 2 − superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated by using both Mellin Transformation and Zeta function. This approximation leads to a universal parameter q for any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameter q . As an application, we extend this concept to the case of Graphene: the reason of this choice is due the existence of an exact mapping about the Dirac oscillator and the compound in question.

Superstatistical properties of the one-dimensional Dirac oscillator

This paper is a reply on the comments of Castanos-Yepes et al, on our paper "Super Statistical properties of the one-dimensional Dirac oscillator" published in Physica A (2020)

Reply on Comments on Superstatistical properties of the one-dimensional Dirac oscillator by Abdelmalek Boumali et al

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Superstatistical properties of the one-dimensional Dirac oscillator

Reply on Comments on Superstatistical properties of the one-dimensional Dirac oscillator by Abdelmalek Boumali et al