Information geometry for the strongly degenerate ideal Bose–Einstein fluid

López-Picón, J.L.; López-Vega, J. Manuel

doi:10.1016/j.physa.2021.126144

Cited by 5 publications

(2 citation statements)

References 33 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%

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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%

“…Note that the ground state contribution to c v appears in the second term of the denominator of (28). Graphs for c v are presented for η = 1 /2 and η = 2 in Fig.…”

Section: Be Statistics For a Finite Number Of Particlesmentioning

confidence: 99%

Bose-Einstein statistics for a finite number of particles

Pessoa

2021

Preprint

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Information geometry and Bose–Einstein condensation

Pessoa

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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It is a long held conjecture in the connection between information geometry (IG) and thermodynamics that the curvature endowed by IG diverges at phase transitions. Recent work on the IG of Bose–Einstein (BE) gases challenged this conjecture by saying that in the limit of fugacity approaching unit—where BE condensation is expected—the curvature does not diverge; rather, it converges to zero. However, as the discontinuous behavior that identifies condensation is only observed at the thermodynamic limit, a study of the IG curvature at a finite number of particles, [Formula: see text], is in order from which the thermodynamic behavior can be observed by taking the thermodynamic limit ([Formula: see text]) posteriorly. This article presents such a study. We find that for a trapped gas, as [Formula: see text] increases, the values of curvature decrease proportionally to a power of [Formula: see text], while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature. This means that, in the thermodynamic limit, the curvature has a limited value where a phase transition is observed, contradicting the forementioned conjecture.

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Bose-Einstein statistics for a finite number of particles

Pessoa

2021

Phys. Rev. A

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Information geometry for the strongly degenerate ideal Bose–Einstein fluid

Cited by 5 publications

References 33 publications

Bose-Einstein statistics for a finite number of particles

Bose-Einstein statistics for a finite number of particles

Information geometry and Bose–Einstein condensation

Bose-Einstein statistics for a finite number of particles

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