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Entropy 2018, 20(10), 773;

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

Departamento de Física, División de Ciencias e Ingenierías Campus León, Universidad de Guanajuato, A.P. E-143, C.P. 37150 León, Guanajuato, Mexico
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 31 August 2018 / Revised: 27 September 2018 / Accepted: 29 September 2018 / Published: 9 October 2018
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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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. View Full-Text
Keywords: superstatistics; Bose–Einstein condensation; Non-Additive Entropies superstatistics; Bose–Einstein condensation; Non-Additive Entropies

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Obregón, O.; López, J.L.; Ortega-Cruz, M. On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases. Entropy 2018, 20, 773.

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