Generalized Entropies Depending Only on the Probability and Their Quantum Statistics

Obregón, O.; Ortega-Cruz, M.

doi:10.3390/ecea-4-05020

Cited by 2 publications

(8 citation statements)

References 8 publications

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“…For completeness, we will exhibit also the corresponding generalized Fermi-Dirac distribution. The differences between the probability distributions that define our entropies (10) and the ones defined by the nonextensive Tsallis q-statistics have been shown in [14]. For values not so far from q = 1, above and below, our distributions behave similarly to those of q-statistics, but they are not exactly equal for any value of q.…”

Section: Generalized Entropiesmentioning

confidence: 75%

“…Temperature is fixed depending on the mass of the particles in consideration. In the next section, we determine what happens with the critical temperature when the Bose ideal gas obeys the generalized statistics determined by the non-extensive entropies [12,14].…”

Section: Usual Quantum Statisticsmentioning

confidence: 99%

“…Superstatistics considers these fluctuations and takes them into account when estimating the probability of the occurrence of a state in a particular configuration. The starting point is the derivation of entropy from a generalized Boltzmann factor [11][12][13][14], and the probability distribution can be deduced by maximizing the corresponding entropy; the particular case of some generalized quantum distributions can be found in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…We will deal with the quantum statistics of two entropies that depend only on the probability [12][13][14]. Some interesting implications of this particular generalized entropy have been studied in [12,[18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…Those thermodynamic properties can be calculated if the probability density of states of the determined energy is known, a probability which can be derived from entropy. We will follow this path in order to estimate the critical temperature where the Bose condensation occurs for a quantum system characterized by the generalized statistics depending only on the probability [12,14]. This analysis has already been considered for the quantum statistics of q-generalized entropies, and quite interesting results arise [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

Obregón

López

Ortega-Cruz

2018

Entropy

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We explore some important consequences of the quantum ideal Bose gas, the properties of which are described by a non-extensive entropy. We consider in particular two entropies that depend only on the probability. These entropies are defined in the framework of superstatistics, and in this context, such entropies arise when a system is exposed to non-equilibrium conditions, whose general effects can be described by a generalized Boltzmann factor and correspondingly by a generalized probability distribution defining a different statistics. We generalize the usual statistics to their quantum counterparts, and we will focus on the properties of the corresponding generalized quantum ideal Bose gas. The most important consequence of the generalized Bose gas is that the critical temperature predicted for the condensation changes in comparison with the usual quantum Bose gas. Conceptual differences arise when comparing our results with the ones previously reported regarding the q-generalized Bose–Einstein condensation. As the entropies analyzed here only depend on the probability, our results cannot be adjusted by any parameter. Even though these results are close to those of non-extensive statistical mechanics for q ∼ 1 , they differ and cannot be matched for any q.

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Section: Generalized Entropiesmentioning

confidence: 75%

Section: Usual Quantum Statisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

Obregón

López

Ortega-Cruz

2018

Entropy

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Olbert’s Kappa Fermi and Bose Distributions

Treumann

Baumjohann

2021

Front. Phys.

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The quantum version of Olbert’s kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play and dominate the microscopic scale but may have macroscopic consequences.

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Generalized Entropies Depending Only on the Probability and Their Quantum Statistics

Cited by 2 publications

References 8 publications

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

Olbert’s Kappa Fermi and Bose Distributions

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