发表机构
Shanghai Normal University; National Astronomical Observatories, Chinese Academy of Sciences（上海师范大学; 中国科学院国家天文台）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将双狭义相对论框架内普朗克尺度下的光子气体热力学拓展至κ-广义统计框架，推导相关热力学量并揭示其随温度及变形参数κ的变化规律，为相对论复杂系统热力学研究提供新视角。
AI 中文摘要
卡尼亚达基斯（即κ-广义）统计力学为描述相对论区域的复杂系统提供了灵活框架，相比标准麦克斯韦-玻尔兹曼统计能预测更丰富的现象学。本工作在双狭义相对论框架内，将普朗克尺度下光子气体热力学的研究拓展至κ-广义统计力学框架。通过采用κ-广义统计方法，推导了普朗克尺度下光子气体的主要热力学量，包括内能U、亥姆霍兹自由能F、压强P、熵S和定容热容C_V。研究发现，这些κ-变形热力学量对变形参数κ具有非平凡依赖性。随后对这些量随温度T的变化进行数值计算，结果表明，当T趋近于普朗克尺度时，κ-变形热力学量相比狭义相对论中的对应量显著被抑制；而在低温区域，由于κ-广义统计的作用，这些量会增强并超过狭义相对论中的对应量。
英文摘要
Kaniadakis, or $κ$-generalized, statistical mechanics provides a flexible framework for describing complex systems in the relativistic regime and predicts a richer phenomenology compared to its standard Maxwell-Boltzmann counterpart. In the present work, we extend the investigation of photon gas thermodynamics at the Planck scale within doubly special relativity to the framework of $κ$-generalized statistical mechanics. By adopting the $κ$-generalized statistical approach, we derive the principal thermodynamic quantities of a photon gas at the Planck scale, including the internal energy $U$, Helmholtz free energy $F$, pressure $P$, entropy $S$, and heat capacity $C_{\rm V}$. We find that these $κ$-deformed thermodynamic quantities exhibit nontrivial dependence on the deformation parameter $κ$. We then numerically evaluate these quantities as functions of temperature $T$, and reveal that, as $T$ approaches the Planck scale, the $κ$-deformed thermodynamic quantities are significantly suppressed relative to those in special relativity, while in the low-temperature regime they are enhanced and exceed their counterparts in special relativity, as a consequence of the $κ$-generalized statistics.
Comments16 pages, 5 figures
