AI 中文总结
通过质量-视界关系推导修正的弗里德曼方程，发现宇宙学可行性严格限制熵的偏离，所有可行模型预测ΛCDM背景。
AI 中文摘要
我们研究了质量-视界关系的宇宙学含义，该关系为热力学一致的一般化视界熵泛函提供了统一框架。利用第一定律的Cai-Kim表述，我们推导了相应的修正弗里德曼方程，并考察了由此产生的背景演化。我们发现，宇宙学可行性严格限制了允许偏离Bekenstein-Hawking面积律的程度：现象学上可接受的场景被限制在标准熵的狭窄邻域内，而更显著的偏离通常会破坏标准的辐射-物质-暗能量序列。幂律纠缠修正可以产生适度的早期暗能量成分，但仅限于参数空间的一个严格受限区域，而量子引力修正被普朗克尺度抑制，在观测上无关紧要。因此，所有可行模型在当前时期都预测了一个类似ΛCDM的宇宙学背景。这些发现表明，仅背景宇宙学就对此类热力学一致的一般化熵构造施加了严格约束。
英文摘要
We investigate the cosmological implications of the mass-to-horizon relation, which provides a unified framework for thermodynamically consistent generalized horizon-entropy functionals. Using the Cai-Kim formulation of the first law of thermodynamics, we derive the corresponding modified Friedmann equations and examine the resulting background evolution. We find that cosmological viability sharply restricts admissible deviations from the Bekenstein-Hawking area law: phenomenologically acceptable scenarios are confined to a narrow neighborhood of the standard entropy, while more pronounced deviations generically spoil the standard radiation-matter-dark-energy sequence. Power-law entanglement corrections can give rise to a moderate early-dark-energy component, but only within a tightly constrained region of parameter space, whereas quantum-gravity corrections are suppressed by the Planck scale and remain observationally irrelevant. Consequently, all viable models predict a $Λ$CDM-like cosmological background at the present epoch. These findings demonstrate that background cosmology alone imposes stringent constraints on thermodynamically consistent generalized entropy constructions of this class.
Comments14 pages, 2 figures
Journal refPhys. Lett. B 880 (2026) 140778
DOI：10.1016/j.physletb.2026.140778
