Information geometry for Fermi–Dirac and Bose–Einstein quantum statistics

Pessoa, Pedro; Cafaro, Carlo

doi:10.1016/j.physa.2021.126061

Cited by 17 publications

(7 citation statements)

References 30 publications

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“…With the numerical inversion of (13a) established and available at [20], further studies on BE condensation for a broad range of quantum systems -whenever the density of states exponent η can be identified -are now possible without relying on the thermodynamic limit nor on specific approximations -the method presented here obtains calculations with arbitrary precision for any value of β and N . Future work may entail a precise calculation for other definitions of BE critical temperature [13,14] and the information geometry of quantum gases [17,28].…”

Section: Discussionmentioning

confidence: 99%

“…3 β < β c it implies n 0 = 0 in the thermodynamic limit. It follows directly that n 0 N = 0, reducing to (17) for β < β c . From implicit differentiation of (13a), it follows that…”

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 96%

“…the extra term 1 2 ωD in the energy of a harmonic trapped particle is ignored, in order to assign zero energy to the ground state -n µ = 0 for all µ. In this case the continuous approximation yields [7,9,15,17,23]…”

Section: Spectrum and Density Of Statesmentioning

confidence: 99%

“…This appendix will derive the thermodynamical quantities of interest -calculated for finite N in ( 26), ( 27) and ( 29) -reduce to the ones presented in the thermodynamic limitrespectively (17), (18) and (21).…”

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 99%

“…As β ≥ β c it implies ξ = 1 in the thermodynamic limit. Substituting β c in ( 16) into ( 26) becomes (17) for β ≥ β c . Analogously, substituting ξ = 1 into (28) and (30) it follows directly that ∂ξ ∂β N,κ = 0.…”

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 99%

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Bose-Einstein statistics for a finite number of particles

Pessoa

2021

Preprint

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This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -namely, the fraction of particles in the ground state and the specific heat -are calculated here exactly in terms of temperature and fugacity. These calculations are complemented by a numerical calculation of fugacity in terms of the number of particles, without taking the thermodynamic limit. The main advantage of this approach is that it does not rely on approximations made in the vicinity of the usually defined critical temperature, rather it makes calculations with arbitrary precision possible, irrespective of temperature. Graphs for the calculated thermodynamical quantities are presented in comparison to the results previously obtained in the thermodynamic limit. In particular, it is observed that for the gas trapped in a 3-dimensional box the derivative of specific heat reaches smaller values than what was expected in the thermodynamic limit -here, this result is also verified with analytical calculations. This is an important result for understanding the role of the thermodynamic limit in phase transitions and makes possible to further study BE statistics without relying neither on the thermodynamic limit nor on approximations near critical temperature.

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Section: Discussionmentioning

confidence: 99%

“…3 β < β c it implies n 0 = 0 in the thermodynamic limit. It follows directly that n 0 N = 0, reducing to (17) for β < β c . From implicit differentiation of (13a), it follows that…”

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 96%

Section: Spectrum and Density Of Statesmentioning

confidence: 99%

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 99%

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 99%

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Bose-Einstein statistics for a finite number of particles

Pessoa

2021

Preprint

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Fermi–Dirac entropy as a measure of electron interactions

Flores-Gallegos

2023

J Math Chem

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In this work, we analyzed a simple chemical reaction using Fermi-Dirac's entropy defined in terms of the Löwdin's occupation numbers, this definition of entropy has not been applied or explored enough in the field of quantum chemistry, in this regard, Fermi-Dirac's entropy maybe a good option to perform works in which the main purpose will be the study or analysis of the effect of the electron interactions. The results presented in this work were complemented by the analysis of the kinetic energy, potential energy, and the variation of the electric potential, along the reaction path, our results suggest that this entropy can be a useful tool to perform studies on electron interactions.

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Quantum field lens coding and classification algorithm to predict measurement outcomes

Alipour¹,

Gulliver²

2023

MethodsX

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Information geometry for Fermi–Dirac and Bose–Einstein quantum statistics

Cited by 17 publications

References 30 publications

Bose-Einstein statistics for a finite number of particles

Bose-Einstein statistics for a finite number of particles

Fermi–Dirac entropy as a measure of electron interactions

Quantum field lens coding and classification algorithm to predict measurement outcomes

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