Thermal properties of Klein–Gordon oscillator in the context of Amelino-Camelia and Magueijo–Smolin doubly special relativity (DSR) frameworks
Boumali A. Jafari N. Shukirgaliyev B. Serdouk F.
October 2025Springer Nature
European Physical Journal C
2025#85Issue 10
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 Cv, as functions of temperature and the deformation scale. Planck-scale corrections produce distinct, theoretically resolvable shifts in both the position and magnitude of the Cv 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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Laboratory of Theoretical and Applied Physics, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
Fesenkov Astrophysical Institute, Almaty, 050020, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, 1096, Azerbaijan
Physics Department, Nazarbayev University, Astana, 010000, Kazakhstan
Energetic Cosmos Laboratory, Nazarbayev University, Astana, 010000, Kazakhstan
K. Zhubanov Aktobe Regional University, Aktobe, 030000, Kazakhstan
Laboratory of Theoretical and Applied Physics
Fesenkov Astrophysical Institute
Al-Farabi Kazakh National University
Center for Theoretical Physics
Physics Department
Energetic Cosmos Laboratory
K. Zhubanov Aktobe Regional University
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