无需暗物质解决星系和星团动力学问题：Tsallis熵作为涌现引力的唯一基础
Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity
AI总结：
研究探讨修正熵模型在星系尺度影响，应用熵力框架于星系相关，发现Tsallis熵是特定广义熵公式，扩展到球状星团研究其行为，预测特定星系团，为区分Tsallis引力与其他理论提供观测检验，表明熵引力范式需基于Tsallis熵。
AI中文摘要：
虽然修正熵模型，如Barrow、Tsallis、Kaniadakis、幂律、对数和Rényi熵，在宇宙学背景中得到了广泛探索，但它们在星系尺度上的影响仍未得到充分检验。这些Bekenstein-Hawking熵的推广编码了量子引力、非广延或分形时空效应，并能改变引力熵与面积的关系。本文表明，当将熵力框架应用于星系旋转曲线和星系团的重子质量时，它唯一地选择了Tsallis熵作为特定的广义熵公式。然后将这种Tsallis修正引力扩展到球状星团，以完成从星系到星系团再到球状星团的结构层次，并研究其作为系统尺度函数的行为。我们将表明，非广延参数与表征引力系统的任何宏观量，如质量、半径、温度或密度，均无相关性。此外，先前已表明，在标准的引力热力学方法中，熵的定义并不明确。采用非广延统计为纠缠提供了基础，从而能够对纠缠熵进行一致的定义。我们预测存在δ = 1的星系团（即其动力学不需要暗物质的星团），类似于在星系和球状星团尺度上已经观测到的δ = i系统。这一预测提供了一个独特的观测检验，以区分Tsallis引力与ΛCDM和MOND。因此，为了使熵引力范式与从球状星团到星系再到星系团的所有尺度上的观测数据相一致，不可避免地需要以Tsallis熵为基础。
英文摘要：
While modified entropy models-such as Barrow, Tsallis, Kaniadakis,Power-law, Logarithmic, and Rényi entropies-have been widely explored in cosmological contexts, their implications on galactic scales remain largely untested. These generalizations of the Bekenstein-Hawking entropy encode quantum gravitational, nonextensive, or fractal spacetime effects and can alter the gravitational entropy-area relation. In this paper, we demonstrate that the entropic force framework, when applied to galactic rotation curves and the baryonic mass of galaxy clusters, uniquely selects Tsallis entropy as the specific generalized entropy formulation. We then extend this Tsallis modified gravity to globular clusters to complete the structural hierarchy from galaxies to galaxy clusters to globular clusters and to investigate its behavior as a function of system scale. We will show that the nonextensive parameter exhibits no correlation with any of the macroscopic quantities characterizing gravitational systems, such as mass, radius, temperature, or density. Furthermore, it has previously been shown that entropy is not well-defined within the standard thermodynamic approach to gravity. The adoption of nonextensive statistics provides a foundation for entanglement, thereby enabling a consistent definition of entanglement entropy. We predict the existence of galaxy clusters with $δ= 1$ (i.e., clusters whose dynamics require no dark matter) analogous to $δ= 1$ systems already observed at galactic and globular cluster scales. This prediction provides a unique observational test to discriminate Tsallis gravity from $Λ$CDM and MOND. Therefore, for the entropic gravity paradigm to be consistent with observational data across all scales-from globular clusters to galaxies to galaxy clusters-it is inevitably required to be built upon \textit{Tsallis} entropy.
