Galaxies Without Dark Matter: What Does Tsallis Entropy Reveal? express
Imagine a pot of boiling water. Toss in a handful of pasta, and it quickly overcooks and clumps into a sticky mess. But in a huge restaurant kettle where the pasta floats freely, each piece stays separate. Galaxies follow a similar pattern: the usual laws of heat (entropy) work when particles barely notice each other, but in a tightly bound gravitational "pot," stars and gas are so interconnected that the familiar rules break down. Bekenstein and Hawking once derived an entropy formula for black holes, but for entire galaxies, it often fails.
Enter Tsallis entropy Tsallis — a way to measure disorder not for proud loners but for systems where everything is tangled, like spaghetti on a plate. The paper tested several such "spaghetti entropies" and found that only Tsallis's version accurately describes how fast galaxies rotate and how gas moves in their clusters. It turns out that the correction introduced by this entropy does not depend on the system's size, mass, or temperature: it acts like a universal seasoning, working equally well for small globular clusters and giant galaxy clusters.
The most intriguing prediction: there should exist galaxy clusters where gravity is fully explained without dark matter — solely through this special entropy. Such "bare" clusters would be a decisive test: if found, they would point to new physics rather than invisible matter. Similar systems have already been observed on the scale of individual galaxies and globular clusters, but now scientists expect them on larger scales as well. So perhaps the familiar pot of pasta hides a clue to the structure of entire clusters: we just need to find the right entropy recipe.
Original abstract
as written by the authors arXiv:2607.19435
While modified entropy models-such as Barrow, Tsallis, Kaniadakis,Power-law, Logarithmic, and R\'{e}nyi 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 $$\delta = 1$$ (i.e., clusters whose dynamics require no dark matter) analogous to $$\delta = 1$$ systems already observed at galactic and globular cluster scales. This prediction provides a unique observational test to discriminate Tsallis gravity from $$\Lambda$$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.
Tsallis entropy originally emerged not in cosmology but in plasma physics and information theory — for describing systems with 'heavy-tailed' distributions, where extreme events occur more often than ordinary statistics predicts.
In Liu Cixin's novel 'The Dark Forest,' civilizations use the laws of physics as weapons — perhaps manipulating entropy on galactic scales would make the perfect tool for cosmic warfare.