Canonical Quantum Statistics and Gravitational Thermodynamics A Pedagogical Treatment of Gravity, Information, and Entropy

Canonical Quantum Statistics and Gravitational Thermodynamics A Pedagogical Treatment of Gravity, Information, and Entropy | Zenodo Skip to main Communities My dashboard Log in Sign up Zenodo is currently experiencing slowness and intermittent outages due to heavy automated traffic from bots and AI crawlers. We are aware of the problem, and our team is focused on stabilizing the service. Thank you for your patience. Published April 30, 2026 | Version v1 Technical note Open Canonical Quantum Statistics and Gravitational Thermodynamics A Pedagogical Treatment of Gravity, Information, and Entropy Authors/Creators Narlagiri, Linga Murthy (Researcher) 1 Show affiliations 1. Tyndall National Institute Description This technical report develops the mathematical and conceptual framework connecting general relativity, quantum field theory in curved spacetime, black-hole thermodynamics, and quantum information. Beginning with the differential-geometric and field-theoretic foundations, it systematically establishes the network of relations linking horizon geometry, entanglement, and gravitational dynamics. The core topics treated are: (i) Hawking's semiclassical theory of black-hole radiation, derived through Bogoliubov analysis and the KMS condition on the Hartle–Hawking state; (ii) the Bekenstein–Hawking entropy and the four laws of black-hole mechanics; (iii) Jacobson's derivation of Einstein's equations as an equation of state on local Rindler horizons, with explicit attention to the role of energy–momentum conservation as an independent input and the cosmological constant as an integration constant; (iv) Wald's Noether-charge formulation of black-hole entropy and its higher-derivative generalisations; (v) the Unruh effect and the observer-dependence of the particle concept; (vi) the AdS/CFT correspondence and the Ryu–Takayanagi formula, together with the Lewkowycz–Maldacena replica derivation; (vii) generalised entropy, the quantum extremal surface prescription, and the island formula in JT gravity coupled to matter; and (viii) the Page curve and what it does and does not establish concerning the black-hole information paradox. The presentation distinguishes carefully between rigorously established results — Hawking temperature, the area theorem, the four laws, the leading-order RT formula, and the FGHMV linearised-Einstein theorem — and active research programmes, including the microscopic origin of the area law, the operational mechanism of information return, holography beyond AdS, and the interpretation of gravity as emergent. Three appendices provide a full Bogoliubov calculation, the Wald Noether-charge construction, and a mathematical reference. Files canonical_quantum_gravity (3).pdf Files (628.5 kB) Name Size Download all canonical_quantum_gravity (3).pdf md5:9d10f539f9a97cedd0774910c7743fcf 628.5 kB Preview Download 42 Views 30 Downloads Show more details All versions This version Views Total views 42 42 Downloads Total downloads 30 30 Data volume Total data volume 23.3 MB 23.3 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords black hole thermodynamics Hawking radiation Bekenstein-Hawking entropy Unruh effect AdS/CFT correspondence Ryu-Takayanagi formula quantum extremal surfaces island formula Page curve Wald entropy Jacobson derivation quantum field theory in curved spacetime holographic entanglement entropy black hole information paradox generalised entropy JT gravity replica wormholes emergent gravity holographic principle entanglement entropy Details DOI DOI Badge DOI 10.5281/zenodo.19923674 Markdown [](https://doi.org/10.5281/zenodo.19923674) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19923674.svg :target: https://doi.org/10.5281/zenodo.19923674 HTML <a href="https://doi.org/10.5281/zenodo.19923674"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19923674.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19923674.svg Target URL https://doi.org/10.5281/zenodo.19923674 Resource type Technical note Publisher Zenodo Languages English Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Citation Export Technical metadata Created April 30, 2026 Modified May 6, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies

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