Photon Gas Thermodynamics with κ-generalized statistics at Planck-Scale
Abstract
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 CV. 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.
Related
- Photon Gas Thermodynamics in Doubly Special Relativity at the Planck Scale
- Classical-to-Quantum Transition in Blackbody Radiation Thermodynamics: Planck's Law without Statistical Assumptions
- Unified description of random motions and generalized Fokker-Planck equations
- Photon-Statistics Control of Strong-Field Rydberg-State Excitation
- Black hole thermodynamics and KK photon quantum corrections in 2D effective dilaton gravity
BibTeX
@misc{yang2026photon,
title = {{Photon Gas Thermodynamics with $κ$-generalized statistics at Planck-Scale}},
author = {Xinyi Yang and Qi Xiong and Guifeng Su and Yi Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00606},
eprint = {2609.00606},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00606},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Photon Gas Thermodynamics with κ-generalized statistics at Planck-Scale
AU - Xinyi Yang
AU - Qi Xiong
AU - Guifeng Su
AU - Yi Zhang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00606
UR - https://arxiv.org/abs/2609.00606
AB - 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_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.
ER -