Thermal behavior of the Klein Gordon oscillator in a dynamical noncommutative space

Ilyas Haouam

doi:10.1038/s41598-025-10118-7

Thermal behavior of the Klein Gordon oscillator in a dynamical noncommutative space

Sci Rep. 2025 Aug 6;15(1):28771. doi: 10.1038/s41598-025-10118-7.

Author

Ilyas Haouam¹

Affiliation

¹ Laboratoire de Physique Mathématique et de Physique Subatomique (LPMPS), Université Frères Mentouri, Constantine, 25000, Algeria. ilyashaouam@live.fr.

Abstract

We investigate the thermal properties of the Klein-Gordon oscillator in a dynamical noncommutative space. These properties are determined via the partition function, which is derived using the Euler-Maclaurin formula. Analytical expressions for the partition function, free energy, internal energy, entropy, and specific heat capacity of the deformed system are obtained and numerically evaluated. The distinct roles of dynamical and flat noncommutative spaces in modulating these properties are rigorously examined and compared. Furthermore, visual representations are provided to illustrate the influence of the deformations on the system's thermal behavior. The findings highlight significant deviations in thermal behavior induced by noncommutativity, underscoring its profound physical implications.

Keywords: Dynamical noncommutative space; Euler-MacLaurin Formula; Klein-Gordon oscillator; Position-dependent noncommutative space; Thermal properties.