AI 中文总结
研究普朗克尺度下双狭义相对论中光子气体热力学，通过马盖若 - 斯莫林公式推导相关函数并数值评估，结果在特定极限下还原为传统表达式，接近普朗克尺度时热力学函数受抑制。
AI 中文摘要
我们研究了双狭义相对论的马盖若 - 斯莫林公式下光子气体的热力学，该框架用普朗克能量量级的与观察者无关的能量尺度增大了光速。我们推导了光子气体的对数巨配分函数及完整的热力学量集，包括亥姆霍兹自由能、内能、熵、压强和热容量，并进行了数值评估。结果在不变能量尺度趋于无穷时平滑地还原为传统狭义相对论表达式。对于接近普朗克尺度的温度，有限截断导致所有热力学函数相对于标准狭义相对论对应物有系统的抑制。
英文摘要
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.
Comments13 pages, 7 figures
