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REVIEW 4 major objections 3 minor 113 references

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

T0 review · 4 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper argues that emergent gravity must be built on Tsallis entropy to fit observations from galaxies to clusters.

desk verdict A real globular-cluster analysis wrapped in an overreaching uniqueness claim that collapses on the force-law prefactor inconsistency. read the letter →

arxiv 2607.19435 v1 pith:UXDLIUDZ submitted 2026-07-21 astro-ph.GA astro-ph.COgr-qc

S. Shamari , A. Sheykhi This is my paper
classification astro-ph.GAastro-ph.COgr-qc
keywords entropicgravityTsallisentropynonextensivethermodynamicsgalacticrotationcurvesgalaxyclustermassesglobularclustersdarkmatteralternativeMOND
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to identify which generalized entropy, if any, can serve as the foundation of entropic gravity once the theory is tested against real astrophysical data. It tests six entropy formulations against galactic rotation curves, X-ray galaxy-cluster masses, and globular-cluster velocity dispersions. It concludes that only Tsallis (nonextensive) entropy reproduces flat rotation curves, recovers the Tully-Fisher relation, and yields the observed cluster masses without dark matter. It predicts that dynamically relaxed galaxy clusters should be observably dark-matter-free, with nonextensive parameter δ = 1. A sympathetic reader would care because this turns a speculative framework into a falsifiable alternative to dark matter and MOND.

What carries the argument

The central object is the Tsallis entropy S = γA^δ, where A is horizon area and δ is the nonextensive parameter. It leads to a modified gravitational force law, F ∝ GMm/r^{2δ} (with a prefactor involving δ), which the paper applies to hydrostatic equilibrium in galaxy clusters and to Jeans modeling of globular clusters. The single parameter δ carries the entire deviation from Newtonian gravity, and its fitted value varies with scale: δ ≈ 0.5 for galaxies, δ ≈ 0.977 for clusters, δ ≈ 1.005 for globulars.

What would settle it

Re-derive the entropic force for S = γA^δ using the same equipartition steps the paper uses for type-I entropies and check whether the prefactor (2δ − 1)/(2 − δ) actually emerges; if not, the reported δ values are artifacts. Observationally, find a well-relaxed galaxy cluster whose mass profile requires δ significantly different from 1 at high significance, contradicting the prediction.

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Extended reading notes

Core claim

Building on the entropic-force idea, the paper classifies alternative entropies into type-I power-law forms and type-II additive corrections, then derives the corresponding modified Newtonian laws. It shows that type-II entropies (Rényi, Kaniadakis, logarithmic) cannot generate flat rotation curves and that Barrow entropy fails at cluster scales, leaving Tsallis entropy S = γA^δ as the only candidate that passes both tests. Fits to 40 X-ray clusters give ⟨δ⟩ = 0.977 ± 0.004, fits to 33 globular clusters give ⟨δ⟩ = 1.0046 ± 0.0025, and galaxies require δ ≈ 0.5. The paper interprets δ as a measure of incomplete violent relaxation and hidden constraints, and predicts the existence of galaxy clu

Load-bearing premise

The fitted cluster and globular δ values rest on the force law F ∝ GMm/r^{2δ} with a prefactor that vanishes at the galactic value δ ≈ 0.5, and the paper never reconciles this law with its own type-I derivation, so the same equations cannot simultaneously produce flat rotation curves and the reported cluster fits.

Editorial extensions

If this is right

  • If the central claim is correct, dark matter is unnecessary on galactic, cluster, and globular scales; emergent gravity would uniquely require nonextensive statistical mechanics.
  • The predicted δ = 1 galaxy clusters provide a sharp observational test that can distinguish Tsallis gravity from both ΛCDM and MOND.
  • The framework explains why a few globular clusters show mild flattening in their velocity-dispersion profiles while most do not, without invoking dark matter.
  • The scale dependence of δ (0.5, 0.977, 1.005) suggests nonextensivity tracks dynamical relaxation state rather than system size or mass.
  • All other tested generalized entropies fail at least one of the two main tests, so if the tests stand, Tsallis entropy is the unique surviving option among them.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If δ truly encodes relaxation history rather than scale, the framework could be tested by comparing δ in relaxed versus merging clusters: relaxed clusters should cluster near δ = 1, while recently merged or disturbed clusters should show larger deviations.
  • The uniqueness claim holds only within the six entropy families considered; a different entropy form outside that set could also fit the data, so 'unique' is contingent on the surveyed space of possibilities.
  • The cluster and globular fits rely on the force law's 1/r^{2δ} scaling; re-deriving the force directly from S = γA^δ using the paper's own type-I derivation would reveal whether the fitted δ values are robust or an artifact of an extra prefactor.
  • The predicted dark-matter-free clusters could be searched for in existing X-ray and weak-lensing surveys, sharpening the prediction by identifying specific candidate clusters expected to show δ ≈ 1.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. This paper tests generalized entropy proposals within the Verlinde entropic-gravity framework against galactic rotation curves, X-ray galaxy-cluster masses, and globular-cluster velocity dispersions. It derives a type-I entropic force for power-law entropies and claims that, among Barrow, Tsallis, Kaniadakis, Rényi, logarithmic, and power-law entropies, only Tsallis entropy survives all tests. The evidence consists of fitted Tsallis parameters: δ≈0.5 for galaxies, ⟨δ⟩=0.977±0.004 for 40 galaxy clusters, and ⟨δ⟩=1.0046±0.0025 for 33 globular clusters. The paper interprets δ as a dynamical indicator of relaxation and predicts the existence of δ=1 galaxy clusters that would be observationally dark-matter-free, concluding that entropic gravity must be built on Tsallis entropy.

Significance. If the central claim were established, this would be a striking result: a single nonextensive entropy parameter would replace dark matter on kiloparsec-to-megaparsec scales and would distinguish emergent gravity from both ΛCDM and MOND. The paper deserves credit for assembling a multi-scale dataset and for presenting explicit fitting formulas. However, the load-bearing force law is internally inconsistent, and the uniqueness argument is circular because δ is fitted per object while competing entropies are not given the same fitting treatment. The observational fits therefore do not support the paper's conclusion as it stands.

major comments (4)
  1. [§II.A, Eq. (46); §III, Eq. (54)] The force law used for all observational fits contradicts the force law derived in the paper. Eq. (46) for type-I entropies, with n=2δ−1 for Tsallis entropy, gives F=GMm/R^{2δ}. Eq. (54), imported from [51], is F=−[(2δ−1)/(2−δ)]GMm/R^{2δ}. At the adopted galactic value δ≈0.5 (Table IV, §III.F), Eq. (54) predicts exactly zero force, so it cannot produce flat rotation curves, the Tully-Fisher relation, or any of the galactic successes claimed in §III. Conversely, if Eq. (46) is the correct Tsallis force, then the cluster mass formula Eq. (68) and the globular-cluster acceleration Eq. (71) contain a spurious prefactor, and all fitted δ values in Tables I and II are changed. The paper never reconciles Eqs. (46) and (54); this is a load-bearing mathematical inconsistency, not a harmless normalization choice.
  2. [§II; §III.A–C; §IV] The central claim that only Tsallis entropy 'passes all tests' is not supported by a model comparison. δ is a free parameter fitted separately for each galaxy cluster and each globular cluster. The alternative entropies are dismissed on the basis of functional forms—e.g., Eqs. (63)–(67)—without being fitted to the same data and compared with a common statistic. The paper itself acknowledges in §IV that δ could be viewed as 'an added degree of freedom... introduced merely to fine-tune and justify the results through post-hoc adjustments,' but it responds only with a no-correlation argument and with the Micro-Macro Correspondence Principle stated in §III. Neither response replaces an out-of-sample prediction or an information-criterion comparison, so the uniqueness conclusion rests on circular reasoning.
  3. [§III.D–E, Table II] The quality of the globular-cluster fits is mixed. Reported reduced chi-squared values include 4.61 for NGC 7078, 3.45 for NGC 6809, and 2.58 for NGC 2808, yet the text in §III.E states that seven Scarpa clusters yield good fits and that only M15 is exceptional. Under the paper's own fitting statistic in Eq. (74), χ²_red>2 for several clusters is not a good fit. The claim that Tsallis gravity 'accurately matches' all 33 clusters is therefore overstated; a re-analysis with a more realistic dynamical model, or with these outliers explicitly treated, is required before the globular-scale success can be accepted.
  4. [§V] The prediction of δ=1 galaxy clusters is an extrapolation, not a consequence of the fitted model. Since δ is a fitted parameter, and the cluster sample already contains values as low as 0.973 (Table I), the statement that 'continuity of the framework implies that clusters with δ=1 should exist' has no quantitative selection criterion. No mapping from relaxation state, age, or dynamical history to δ is specified before fitting. As presented, the prediction is not falsifiable in advance; the authors would need to identify which clusters should have δ=1 independently of the fit.
minor comments (3)
  1. [Fig. 1 and captions] The figure contains multiple internal inconsistencies: panels (e) and (f) report R²=0.855, RMSE=0.0016, and a mean of 0.9755 that are not discussed in the text, while the text states ⟨δ⟩=0.977. Several distinct blocks are all labeled 'FIG. 1'. These presentation issues should be fixed.
  2. [Figs. 5–8 captions] The captions use 'b' instead of δ (e.g., 'b=0.9798') and contain typographical temperature entries such as '8 × 1160415 K', which should be 8.0 keV or the equivalent in K.
  3. [§II, Eq. (30)] The derivation of the power-law correction is dimensionally unclear: setting ∂f/∂R=R^3/(GM) makes f depend on the source mass M, while the subsequent conclusion S∼A² is presented as a general result. This needs clarification.

Circularity Check

2 steps flagged · score 6.0 of 10

Central 'Tsallis uniqueness' rests on a self-cited force law (Eq. 54) that contradicts the paper's own derivation (Eq. 46), plus a δ=1 cluster 'prediction' that is a restatement of fitted δ values.

  1. self citation load bearing [Section III, Eq. (54)]
    "the modified Newton's law of gravity inspired by Tsallis entropy is given by [51] F = −[(2δ − 1)/(2 − δ)] GMm/R^{2δ} ... The effectiveness of the above relation in explaining galactic rotation curves has been demonstrated in [51]."

    The paper's own type-I derivation, Eq. (46), gives F = GMm/R^{n+1} with n = 2δ−1, i.e., F = GMm/R^{2δ} with no (2δ−1)/(2−δ) prefactor. That prefactor vanishes at the galactic value δ ≈ 0.5 adopted in Table IV, so Eq. (54) cannot produce flat rotation curves at the paper's own galactic δ. The paper never reconciles Eqs. (46) and (54); it simply imports Eq. (54) from [51], authored by co-author A. Sheykhi. All cluster (Eq. 68) and globular (Eq. 71) fits inherit this self-cited prefactor, so the uniqueness conclusion is justified by a self-citation rather than by the paper's own derivation.

  2. fitted input called prediction [Section V, Prediction of Dark Matter-Free Galaxy Clusters]
    "Since δ is a dynamical measure of the relaxation state, and since relaxed systems (globular clusters, post-collapse simulated states) exhibit δ ≈ 1, it follows that galaxy clusters that have undergone sufficient dynamical relaxation should also exhibit δ ≈ 1. Such clusters would be observationally dark matter-free, as their dynamics would be fully described by baryonic mass alone."

    δ is a free parameter fitted independently to each system (Eq. 74 for globulars; effectively Eq. 68 for clusters). The 'prediction' of δ = 1 clusters is an extrapolation from the already-fitted range (0.973–1.067) and from the interpretive claim that relaxed systems have δ ≈ 1. By construction, δ = 1 makes the Tsallis force Newtonian, so a δ = 1 cluster is 'dark matter-free' by definition. The prediction is thus a restatement of the fitted parameter distribution, not an independent consequence of Tsallis entropy.

full rationale

The paper contains genuine new empirical work — fitting Tsallis δ to 40 galaxy clusters and 33 globular clusters, and comparing with other entropies — and that part is not circular. However, the central uniqueness claim is partially circular. First, the Tsallis force law used for all fits, Eq. (54), is quoted from [51], by co-author A. Sheykhi, and is inconsistent with the paper's own type-I derivation, Eq. (46), which gives no (2δ−1)/(2−δ) prefactor; at the adopted galactic δ ≈ 0.5 the prefactor vanishes, so the same law cannot explain flat rotation curves. The paper never reconciles the two laws, so the galactic-scale success and the uniqueness conclusion rest on a self-citation rather than on the paper's own derivation. Second, the headline prediction of dark-matter-free clusters with δ = 1 is a statement about the range of fitted δ values, not an independent theoretical prediction: δ = 1 is defined as Newtonian, and the predicted class is essentially the fitted parameter range. The paper itself flags the key objection, noting 'one might suspect that this extra parameter is nothing more than an added degree of freedom, introduced merely to fine-tune and justify the results through post-hoc adjustments' (Section IV). The response relies on external simulations and the fitted distribution, which does not remove the circularity. These issues make the central claim partially circular, though the cross-entropy comparison and the new cluster/globular fits are independent content, so the score is 6 rather than higher.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the Verlinde framework, an ad hoc correspondence principle, a β-model isothermal cluster assumption, an isotropic Hernquist globular model, and one free fitted exponent δ per system (40 clusters, 33 globulars, plus δ≈0.5 borrowed for galaxies). No new particles or forces are introduced; the 'zero-energy bits' mechanism is cited from prior work.

free parameters (3)
  • δ (galaxy clusters) = 0.955–0.983, mean 0.9770 ± 0.004 (Table I)
    Fitted per cluster to match X-ray mass profiles via Eq. (68). No prior or independent determination; any mismatch between the β-model baryonic mass and observed mass is absorbed by δ.
  • δ (globular clusters) = 0.973–1.067, mean 1.0046 ± 0.0025 (Table II)
    Fitted per cluster to velocity dispersion profiles via Eq. (74). Central to the claim that globulars are essentially Newtonian.
  • δ (galaxies) = ≈ 0.5
    Taken from prior work [51] and used as the galactic-scale anchor for the uniqueness argument. Not re-derived or fitted in this paper.
assumptions (6)
  • domain assumption Verlinde's entropic gravity framework: gravitational force emerges from holographic screen thermodynamics with N=4S and equipartition E=(1/2)NT.
    All force laws (Eqs. 41, 46, 54) rest on this framework; the paper does not derive it.
  • domain assumption Tsallis entropy S=γA^δ is the correct generalization of horizon entropy for gravitational systems.
    Used everywhere; motivated by nonextensivity but not derived in this paper.
  • ad hoc to paper Micro-Macro Correspondence Principle, introduced in Section III: success at one scale implies microscopic validity of the same entropy.
    This principle is introduced in this paper to justify interpreting fitted δ values as evidence about quantum spacetime; it is not an established physical theorem.
  • domain assumption Cluster gas is isothermal and follows the King β-model in hydrostatic equilibrium (Eqs. 55–62).
    Used to convert X-ray surface brightness and temperature into gravitational acceleration; violations such as cool cores or asphericity would shift fitted δ.
  • domain assumption Globular clusters are isotropic, single-mass Hernquist spheres with masses from Baumgardt & Hilker; the Jeans equation (72)–(73) applies.
    Used for all 33 globular fits; the paper acknowledges in Section III.F that anisotropy and multimass effects could change the fits.
  • domain assumption The entire mass discrepancy in clusters is attributable to the Tsallis force law with a single δ per cluster, i.e., no dark matter and no temperature/density profile systematics.
    Needed to interpret the δ fits as a test of entropy rather than as absorption of modeling error; not tested against a dark-matter baseline.

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Cite this review

Pith. "Pith review of Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity." pith.science (2026). https://pith.science/paper/UXDLIUDZ

@misc{pith2026260719435,
  author       = {Pith},
  title        = {Pith review of: Resolving Galactic and Cluster Dynamics Without Dark Matter: Tsallis Entropy as the Unique Foundation of Emergent Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UXDLIUDZ}},
  note         = {Machine review of arXiv:2607.19435}
}
abstract

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.

Figures

Figures reproduced from arXiv: 2607.19435 by the authors.

Figure 2
Figure 2. FIG. 2: Scatter plot of the Tsallis parameter [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4: (a) Three-dimensional distribution of the nonexten [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. FIG. 5: Galaxy cluster A0401 radial mass as function of ra [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figures from the paper (4 more)
Figure 6
Figure 6. Figure 6: FIG. 6: Galaxy cluster A0478 radial mass as function of ra [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Galaxy cluster A0754 radial mass as function of [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Galaxy cluster A0400 radial mass as function of ra [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Line of sight velocity dispersion profiles for se [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]

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