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arXiv · 2511.11709

Thermal properties of Klein-Gordon Oscillator in the Context of Amelino-Camelia and Magueijo-Smolin Doubly Special Relativity (DSR) frameworks

Abdelmalek Boumali·Nosratollah Jafari·Bekdaulet Shukirgaliyev·Fadila Serdouk
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Abstract

We examine the thermal and statistical properties of the one dimensional Klein-Gordon oscillator within two prominent Doubly Special Relativity (DSR) frameworks: Amelino-Camelia and Magueijo-Smolin. Using the modified dispersion relations specific to each formulation, we derive the positive energy spectra, construct the partition function via the Euler-Maclaurin method, and compute key thermodynamic quantities, including the specific heat $C_v$, as functions of temperature and the deformation scale. Planck-scale corrections produce distinct, theoretically resolvable shifts in both the position and magnitude of the $C_v$ peak in the two models. An accompanying entropy analysis reveals that these peaks correspond to smooth Schottky-type anomalies: the specific heat curves remain analytic and positive across the explored temperature range, and thus do not indicate latent or continuous thermodynamic phase transitions. These comparative results provide a robust diagnostic framework for differentiating DSR prescriptions in relativistic quantum systems and reinforce the transition-free character of their thermal response.

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Abdelmalek Boumali, Nosratollah Jafari, Bekdaulet Shukirgaliyev, Fadila Serdouk. 2025-11-12. Thermal properties of Klein-Gordon Oscillator in the Context of Amelino-Camelia and Magueijo-Smolin Doubly Special Relativity (DSR) frameworks. https://doi.org/10.1140/epjc%2Fs10052-025-14892-6

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