Entropic gravity models, which imply that gravity is an emergent law of physics, rather than a fundamental force in its own right, are a very attractive possibility from a reductionist perspective. This paper looks at an entropic gravity theory that would eliminate the need for dark matter and suggests a way to observationally distinguish it from ΛCDM and MOND models. It doesn't work out the cosmological implications of the theory, however, although since it replicates MOND in other contexts, it can be expected to be similar to it in the area of cosmology.
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 Tsallis entropy.
S. Shamari, A. Sheykhi, "Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity" arXiv:2607.19435 (July 21, 2026).
The introduction to this paper in the body text provides context for the entropic gravity concept, which is follows by subsequent sections that lay out the equations implied by the theory and by its competing explanations of dark matter phenomena in detail:
The quest to understand the fundamental nature of gravity, space, and time has led to profound theoretical innovations, among which the thermodynamic-gravity conjecture stands as a pivotal insight. Originally formulated by Jacobson and later enriched by Padmanabhan’s emergence paradigm, this conjecture posits that gravitational field equations-including those of General Relativity-can be derived from thermodynamic principles applied to spacetime horizons. In this framework, the Bekenstein-Hawking entropy S = A/(4G) plays a central role, linking the geometry of horizons to the statistical mechanics of spacetime microstates. In recent years, however, various quantum-gravitational, nonextensive, and fractal-spacetime considerations have motivated generalizations of this entropy formula, giving rise to modified entropy prescriptions such as those of Barrow, Tsallis, Kaniadakis, Power-law, Logarithmic and Rényi. These extended entropies introduce new parameters that encode departures from standard thermodynamics and may reflect deep-seated quantum or geometric properties of spacetime.
To date, research on modified entropies has been predominantly cosmology-centric. Studies have explored how such corrections alter the Friedmann equations, influence dark energy models, modify inflationary scenarios, and leave imprints on the cosmic microwave background.
While these investigations have placed valuable constraints on entropy parameters using large-scale cosmological data, a critical and largely uncharted frontier remains: how do modified entropies manifest on galactic and sub-cosmological scales?
Galaxies-and the dark matter halos that host them-represent gravitational systems with well-defined effective horizons and rich dynamical observables (rotation curves, velocity dispersion profiles, baryonic mass-velocity relations). Yet, the implications of horizon thermodynamics for such systems have scarcely been explored, leaving open the question of whether galactic kinematics can serve as a new, independent test bed for quantum-gravitational entropy corrections.
Our aim here is to bridge this gap by developing and applying a framework to test modified entropies through galactic-scale observations. We posit that if horizon thermodynamics underpins gravitational dynamics, then the entropy associated with the boundary of a galaxy or a dark matter halo-be it the Hubble radius of a galaxy group or the radius enclosing a fixed density contrast should govern its equilibrium properties. Using the entropic force scenario proposed by Verlinde [1] we derive modified force laws and mass-velocity relations that depend explicitly on the chosen entropy form. These relations can then be confronted with high-precision galactic data from surveys such as SPARC (for rotation curves), MaNGA (for stellar kinematics), and other spatially resolved kinematic datasets.
Although the origins of the dark matter problem trace back to the early 1930s with the work of Zwicky and Oort, it only became a hot research topic when Vera Rubin published her observations of galactic rotation curves. Today, after nearly a century of diverse astrophysical observations from the dynamics of galaxy clusters to gravitational lensing studies and baryon acoustic oscillations a consistent picture emerges: approximately 85% of the matter in the universe is non-baryonic. Despite extensive searches, direct detection of dark matter particles remains elusive, motivating serious consideration of alternative ideas [2–7].
Many different theories have been proposed to explain this puzzle without non-baryonic dark matter such as Modified Gravity (MOG), Modified Newtonian Dynamics (MOND), Carmelian theory, Cooperstock model, etc [8–12].
Deur does not get a mention, although his approach deserves it. References [8-12] are:
[8] J. W. Moffat, Scalar-Tensor-Vector Gravity Theory, J. Cosmol. Astropart. Phys. 2006, 004 (2006).
[9] M. Milgrom, A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis, Astrophys. J. 270, 365 (1983).
[10] F. I. Cooperstock and S. Tieu, Galactic dynamics via general relativity: A compilation and new developments, Int. J. Mod. Phys. A 22, 2293 (2007).
[11] M. Carmeli, Is Galaxy Dark Matter a Property of Spacetime?, Int. J. Theor. Phys. 37, 2621 (1998).
[12] S. Behar and M. Carmeli, Derivation of the Tully-Fisher Law from General Relativity Theory: Doubts about the Existence of Halo Dark Matter, Int. J. Theor. Phys. 39, 1397 (2000).
A parallel line of inquiry emerged from black hole thermodynamics, following the discovery that black holes possess entropy proportional to their horizon area and temperature. Jacobson demonstrated that the Einstein field equations are nothing but an equation of state for spacetime. Verlinde’s entropic gravity framework realizes the idea that gravity itself may be an emergent phenomenon, with spacetime possessing intrinsic thermodynamic properties. In this thermodynamic paradigm, the choice of entropy functional becomes crucial. While Bekenstein-Hawking entropy leads to standard general relativity, any alternative entropy yields modified gravitational dynamics [13–16].
In this work, we classify all possible entropy modifications into two types of generalized entropies. We first examine their performance in reproducing galactic rotation curves; in this assessment, only Tsallis entropy succeeds. Next, we investigate their performance in galaxy clusters. We reconstruct a well-known model and again evaluate each modified entropy. Once more, Tsallis entropy emerges successful. We then extend this Tsallis modified gravity to globular clusters to complete the structural hierarchy. After analyzing and plotting the corresponding figures, we turn to the origin of Tsallis entropy and its theoretical implications.
This paper is structured as follows. Section II critically examines type-II entropies, demonstrating their failure at galactic and cluster scales. In Section III, we derive the Tsallis-modified force law and apply it to galaxy clusters, presenting our observational analysis of 40 clusters. We then extend this framework to globular clusters, analyzing the velocity dispersion profiles of 33 such systems. In Section IV, we discuss the theoretical foundations of nonextensive statistics in gravitational systems, drawing on the work of Chavanis and others, and interpret the physical meaning of the Tsallis parameter δ in terms of dynamical relaxation and hidden constraints. Section V presents our central prediction: the existence of dynamically relaxed galaxy clusters that are observationally dark matter-free, offering a decisive test to distinguish Tsallis gravity from ΛCDM and MOND. Finally, Section VI is devoted to closing remarks. Throughout this paper we set ℏ = c =kB =1.
Another notable new paper on galactic dynamics, which has phenomenological merit, but is probably flaws in its mechanism is:
We investigate whether the observed fine structure and asymmetry of non-averaged galactic rotation curves can be reconstructed directly from the observed HI distribution within the framework of a kinetic gas transport description. Using the observed HI density profiles separately for the approaching (north-eastern) side and the receding (south-western) side of the galaxy NGC~3198, we reconstruct the corresponding rotation curves based on the equation previously derived in Lipovka 2022. It is shown that the reconstructed curves reproduce not only the approximately flat large-scale behaviour of the observed rotation curves, but also their detailed local morphology and asymmetry separately for the north-eastern and south-western sides of the galactic disk. The obtained results indicate that the local structure of galactic rotation curves is closely connected with the local HI distribution and arises naturally as a consequence of kinetic gas transport processes in galactic disks.
Anton A. Lipovka, Anna A. Lipovka "Local morphology and asymmetry of galactic rotation curves in a kinetic gas transport framework: NGC 3198" arXiv:2607.19505 (July 21, 2026).
The abstract of Lipovka 2022 is as follows:
In this paper, I show that generally accepted methods of classical mechanics are not applicable for calculating the outer parts of the rotation curves of galaxies, where an influence of collisions on gas dynamics becomes dominant. In addition, the hydrodynamic approach cannot be used for this purpose due to an extreme rarefaction of the gas. I develop a new approach to describing the gas dynamics in outer regions of galactic disks, where the gas dynamics is determined mainly by collisions.
Equations (free from restrictions imposed on hydrodynamics) are obtained that describe the dynamics of rarefied gas. The resulting equations relate two quantities: the tangential velocity of the gas as a function of the distance from the center of a galaxy (rotation curve) and the radial distribution of the gas density. It is shown that if the physical properties of the rarefied gas are properly taken into account, then dark matter is not required, and the "nonphysical" (non-Keplerian) rotation curves of the outer parts of the galactic disks are tailwinds that can be described within the framework of conventional gas kinetics.
To illustrate the correctness of the obtained model, two galaxies with flat rotation curves (NGC7331 and NGC3198) are considered. From the observed rotation curves, using Eq. (14), the radial densities of the gas are calculated. An excellent agreement was obtained between the calculated gas densities and their observed values, which is a serious argument in favor of the developed model. Thus, the non-physical rotation curves of spiral galaxies represent the tailwinds of gas, the dynamics of which is naturally described by the kinetic equation without involving the concept of dark matter. The total masses of two galaxies NGC7331 and NGC3198 have been calculated. The implications for cosmology are discussed.
This theory purports to explain MOND dynamics without either particle dark matter or modified gravity, using interstellar, apparently basically baryonic, gas dynamics. Any theory that works without significant new physics deserves serious attention, but I'm skeptical that it really describes the mechanism of dark matter phenomena.
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