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

TL;DR

This paper investigates how the thermal properties of the Klein-Gordon oscillator are affected by two DSR frameworks, revealing distinct shifts in thermodynamic behavior due to Planck-scale modifications.

Contribution

It provides a comparative analysis of the thermal behavior of the Klein-Gordon oscillator within Amelino-Camelia and Magueijo-Smolin DSR models, highlighting Planck-scale effects.

Findings

Planck-scale corrections cause shifts in the specific heat peak.

Specific heat curves show smooth Schottky-type anomalies.

No thermodynamic phase transitions are observed.

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.