A LARGER ESTIMATE OF THE ENTROPY OF THE UNIVERSE
Open accessAbstract
Using recent measurements of the supermassive black hole (SMBH) mass function, we find that SMBHs are the largest contributor to the entropy of the observable universe, contributing at least an order of magnitude more entropy than previously estimated. The total entropy of the observable universe is correspondingly higher, and is S obs = 3.1 +3.0 −1.7 × 10 104 k . We calculate the entropy of the current cosmic event horizon to be S CEH = 2.6 ± 0.3 × 10 122 k , dwarfing the entropy of its interior, S CEH int = 1.2 +1.1 −0.7 × 10 103 k . We make the first tentative estimate of the entropy of weakly interacting massive particle dark matter within the observable universe, S dm = 10 88 ± 1 k . We highlight several caveats pertaining to these estimates and make recommendations for future work.
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The total coarse-grained entropy in the observable Universe is Stotobs≈(5.9+4.1+2.0+3.1×10^14)×10^88.
“Stotobs≃Sγ+Sν+SIGM+SBH≈(5.9+4.1+2.0+3.1×1014)×1088”
From Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe (2025) · cites this paper as [40]
Section 2.7 reports supermassive-black-hole entropy of 3.1 × 10^104 k, supporting the dominant term and approximate total. But Sections 2.2 and 2.3 give photon and neutrino entropies of 2.03 × 10^89 k and 5.16 × 10^89 k, not the claimed 5.9 × 10^88 and 4.1 × 10^88. Section 2.1 estimates combined interstellar and intergalactic gas entropy at 7.1 × 10^81 k, not the claimed IGM term. (LLM, conf=0.90)
Experimental — accuracy not yet measuredEquation (9) agrees with the benchmark compilation Stotobs=(3.1±0.3)×10^104 by Egan and Lineweaver.
“Equation (9) agrees with the benchmark compilation Stotobs=(3.1±0.3)×10104 by Egan and Lineweaver [40].”
From Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe (2025) · cites this paper as [40]
Section 2.7 (page unavailable) gives an entropy estimate of 3.1 × 10^104 k for supermassive black holes, consistent with the claimed central value. But its uncertainty is asymmetric, +3.0/−1.7 × 10^104 k, not ±0.3 × 10^104; the quoted benchmark is therefore not accurate. (LLM, conf=0.94)
Experimental — accuracy not yet measuredThe higher Egan and Lineweaver entropy value includes dark matter phase-space entropy, which QMM excludes because it is represented separately as imprint entropy.
“(Their higher value includes dark matter phase-space entropy, which we exclude because in QMM it is represented separately as imprint entropy.)”
From Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe (2025) · cites this paper as [40]
Section 2.5 (page unavailable) includes an estimate of dark-matter entropy in the observable universe, but derives it from assumptions about dark-matter decoupling; it does not identify the estimate as phase-space entropy. Section 2.7 (page unavailable) attributes the higher overall entropy estimate to a larger supermassive-black-hole contribution. The statement about QMM's imprint entropy is the citing authors' own explanation, not a claim established by this source. (LLM, conf=0.86)
Experimental — accuracy not yet measuredEgan and Lineweaver (2010) found a numerical value for the de Sitter event horizon entropy, given in Eq. (5).
“Taking into account the present uncertainties in the cosmological data, Egan and Lineweaver (2010) found from this the following numerical value:”
From On a quantum Weyl curvature hypothesis (2022) · cites this paper as Egan and Lineweaver (2010)
Section 3, Eq. (40), gives a numerical entropy with uncertainty, 2.6 ± 0.3 × 10^122 k, for the present cosmic event horizon. It does not identify that value as the entropy of the asymptotic de Sitter horizon; Section 3 says the horizon is still growing toward its future size. (LLM, conf=0.83)
Experimental — accuracy not yet measuredThe biggest contribution to non-gravitational entropy comes from CMB photons, with a slightly smaller value for relic neutrinos.
“the biggest contribution to non-gravitational entropy comes from the CMB photons, with the value”
From On a quantum Weyl curvature hypothesis (2022) · cites this paper as Egan and Lineweaver (2010)
Section 2.2 calls CMB photons the most significant non-black-hole entropy contributor, and Sections 2.2–2.3 give relic neutrinos a slightly lower entropy density than CMB photons. However, the total entropy values printed in those sections put relic neutrinos above CMB photons, so the claimed ranking of their total contributions is not consistently supported by our copy. (LLM, conf=0.82)
Experimental — accuracy not yet measured
The best estimates of the current entropy give numbers of order 10^103.
“The best estimates of the current entropy give numbers of order 10 103 [12].”
From In What Sense Is the Early Universe Fine-Tuned? (2014) · cites this paper as [12]
The paper’s Abstract gives an estimate of about 10^103 k for the entropy inside the current cosmic event horizon. But its estimate for the present observable universe is 3.1 × 10^104 k, and the event horizon itself has still greater entropy. The unqualified claim omits which entropy budget the 10^103 figure describes. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe amount of entropy presently associated with supermassive black holes outweighs that of ordinary matter by a factor 10^15.
“Now, as a matter of fact, the amount of entropy presently associated with supermassive black holes outweighs that of ordinary matter by a factor 10 15 (see e.g.[43]).”
From Conformal Cyclic Cosmology, gravitational entropy and quantum information (2023) · cites this paper as [43]
Section 2.7 estimates present supermassive-black-hole entropy at 3.1 × 10^104 k. Section 2.2 puts CMB photon entropy at about 2 × 10^89 k, giving a ratio on the order of 10^15. But if “ordinary matter” means baryonic matter, Section 2.1 estimates only about 10^81–10^82 k for stars and gas, so the stated factor does not apply to that comparison. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe non-gravitational entropy of the Universe is completely negligible compared to the gravitational entropy.
“We see that the non-gravitational entropy is completely negligible.”
From On a quantum Weyl curvature hypothesis (2022) · cites this paper as Egan and Lineweaver (2010)
The dominating gravitational contributions to entropy are supermassive black holes, followed by stellar black holes.
“The dominating contributions from the gravitational side are supermassive black holes (SMBHs), followed by stellar black holes.”
From On a quantum Weyl curvature hypothesis (2022) · cites this paper as Egan and Lineweaver (2010)
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“A similar argument applies to the case with one black hole using (3).”
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- Authors
- Egan, C. A., & Lineweaver, C. H.
- Affiliations
- Australian National University (AU)
- Corresponding author
- Egan, Chas A.
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 2010-02-03
- Volume
- 710
- Issue
- 2
- Pages
- 1825-1834
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W2100463561
- Cited by
- 232
- References
- 48
- Citations by year
- 2026: 15 · 2025: 43 · 2024: 6 · 2023: 24 · 2022: 17 · 2021: 15 · 2020: 9 · 2019: 12 · 2018: 4 · 2017: 14 · 2016: 15 · 2015: 8 · 2014: 9 · 2013: 15 · 2012: 10
- FWCI
- 6.97
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Astrophysical Journal (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- ANU Open Research (Australian National University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Keywords
- supermassive black holes, cosmic event horizon, WIMPs, black hole entropy
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