Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy

[2608.27721] Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy Skip to main content Search Submit Donate Log in General Relativity and Quantum Cosmology arXiv:2608.27721 (gr-qc) [Submitted on 27 Aug 2026] Title: Thermodynamic Criticality in FLRW Cosmology with Non-extensive Loop Quantum Gravity Entropy Authors: Miguel Cruz , Joel Saavedra , Juan Rodriguez View PDF HTML (experimental) Abstract: We investigate thermodynamic criticality in a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker universe with a non-extensive Loop Quantum Gravity inspired entropy on its apparent horizon. Using the full Kodama-Hayward temperature and the unified first law, we derive the modified Friedmann dynamics and construct the corresponding horizon equation of state. We see that a finite physical critical point only appears in the non-extensive branch $q>1$, while in the Bekenstein-Hawking limit $q\to1$, the critical point is continuously pushed to $v_c\to\infty$ and $T_c\to0$. Along the same spinodal curve, both the constant-pressure heat capacity and the isothermal compressibility become unbounded, and the extremum of this curve is located at the critical point. Below the critical temperature, the Gibbs free energy develops several thermodynamic branches, and the phase coexistence for different horizon states is verified by the equality of temperature, pressure, and Gibbs free energy. The critical exponents are $(\alpha_{cr},\beta_{cr},\gamma_{cr},\delta_{cr}) =(0,1/2,1,3)$, indicating that the system belongs to the standard mean-field universality class despite the non-algebraic form of the equation of state. The normalized Ruppeiner curvature diverges precisely on the spinodal curve and shows critical scaling $R_N\sim-|v-v_c|^{-4}$ on the critical isotherm, and $R_N\sim-|t|^{-2}$ on the critical isochore. Finally, the critical expansion scale is given by $H_c^2=2(\sqrt{5}-2)|\beta|$, which implies that the thermodynamic critical point occurs when the entropy deformation is of order unity. These results establish a self-consistent critical structure for the effective thermodynamic state space of the cosmological apparent horizon and retain the mean-field critical universality. Comments: 23 pages, 8 figures Subjects: General Relativity and Quantum Cosmology (gr-qc) ; High Energy Physics - Theory (hep-th) Cite as: arXiv:2608.27721 [gr-qc] (or arXiv:2608.27721v1 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2608.27721 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Joel Saavedra [ view email ] [v1] Thu, 27 Aug 2026 21:25:52 UTC (588 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2026-08 Change to browse by: hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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