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arXiv:2508.12124

Universal Thermodynamics of Dunkl-Deformed Bose Gases: From Power-Law Traps to Physical Bounds

Medani, M., Mohamed Benarous, A. Hocine, F. Merabtine

Published Aug 16, 2025• 0 citations
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Abstract

We study an ideal Bose gas confined by a $D$-dimensional power-law potential within the framework of the Dunkl formalism. By analyzing the combined effects of spatial dimensionality and trap geometry, we derive universal expressions for the thermodynamic quantities, which depend solely on a single parameter. This reduction reveals the existence of universality classes that apply to any power-law potential, regardless of its specific form.

DOI
10.48550/arxiv.2508.12124

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We study an ideal Bose gas confined by a DDD-dimensional power-law potential within the framework of the Dunkl formalism. By analyzing the combined effects of spatial dimensionality and trap geometry, we derive universal expressions for the thermodynamic quantities, which depend solely on a single parameter. This reduction reveals the existence of universality classes that apply to any power-law potential, regardless of its specific form.
Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in ddd dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.
The use of the Dunkl derivative, defined by a combination of the difference-differential and reflection operators, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address another essential problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit andfinally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions.
Abstract By examining the internal energy and the heat capacity of a harmonically trapped ideal Bose gas within the Dunkl formalism, we show that the Wigner parameter influences the slopes of these thermodynamic functions in the critical region, reflecting its role in modifying the statistical properties of the system. However, despite these modifications, the phase transition itself retains the same order and critical exponents as in the standard case, in accordance with symmetry arguments. Furthermore, upon analyzing the classical behavior, we establish both upper and lower bounds for the Wigner parameter by ensuring thermodynamic consistency in different temperature regimes.
The critical temperature for Bose-Einstein condensation, ground-state fraction, and heat capacity of an ideal gas of Bose particles that are confined by an n-dimensional generic power-law potential trap are derived. The conditions for Bose-Einstein condensation and the discontinuous conditions of the heat capacity at critical temperature are obtained. All these quantities and conditions are found to vary markedly with the dimensionality of space, characteristics of particles, and shape of the external potential. The results obtained here are universal.
The density of states and thermodynamic properties of an ideal gas system trapped in a generic power-law potential in an n -dimensional space are studied. A unified description for the Bose, Fermi and classical gases is given by using the grand potential of the system. Consequently, not only the results in current textbooks of statistical mechanics but also some new general important conclusions, such as the conditions for the occurence of Bose-Eisntein condensation in a trapped Bose system in any dimensional space, can be derived directly using the results of this paper.