Photon Gas Thermodynamics in Doubly Special Relativity at the Planck Scale

We investigate the thermodynamics of a photon gas within the Magueijo-Smolin formulation of doubly special relativity, a framework that augments the speed of light with an observer-independent energy scale of the order of the Planck energy. We derive the logarithmic grand partition function, and the complete set of thermodynamic quantities for the photon gas, including the Helmholtz free energy, internal energy, entropy, pressure, and heat capacity, and perform their numerical evaluation. Our results smoothly reduce to the conventional special relativistic expressions in the limit where the invariant energy scale tends to infinity. For temperatures approaching the Planck scale, the finite cutoff induces a systematic suppression of all thermodynamic functions relative to their standard special-relativistic counterparts.