Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity

@misc{shamari2026resolving,
  title = {{Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity}},
  author = {S. Shamari and A. Sheykhi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.19435},
  eprint = {2607.19435},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.19435},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity
AU  - S. Shamari
AU  - A. Sheykhi
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2607.19435
UR  - https://arxiv.org/abs/2607.19435
AB  - 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 ΛCDM 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.
ER  -