Skip to main Communities My dashboard Log in Sign up Entropy- Originated Framework for a Unified Theory of Matter and Gravity: A Diagram Hilbert Space Framework Published April 11, 2026 | Version v1 Preprint Open Emergent Entropic Gravity from Non-Commutative Operator Dynamics: A Unified Framework for Galaxy Dynamics, Clusters, and Cosmology Authors/Creators Arneth, Borros (Researcher) 1, 2 Show affiliations 1. Philipps University of Marburg 2. Justus-Liebig-Universität Gießen Description We develop a covariant operator–entropic framework in which gravitational dynamics emerge from a non-commutative microscopic algebra through coarse-graining and entropy extremization. The theory is formulated on a diagrammatic Hilbert space with non-commuting operators associated with energy and conserved charges, and macroscopic observables are obtained via completely positive trace-preserving maps. At leading order, the extremization of an effective entropy functional reproduces Einstein–Maxwell dynamics. Subleading corrections induced by non-commutativity generate an emergent acceleration scale a0 , yielding a modified weak-field force law and a logarithmic contribution to the gravitational potential. We construct a covariant completion in which the entropic sector contributes an effective stress–energy tensor, allowing consistent treatment of gravitational lensing, galaxy clusters, and cosmological evolution. The resulting framework reproduces flat galactic rotation curves and the radial acceleration relation, while providing additional gravitational support at cluster scales without invoking particle dark matter. At the background and linear level, the model admits a ΛCDM-like expansion history, ensuring consistency with cosmic microwave background observations. We derive the equations necessary for numerical implementation and outline observational tests using galaxy rotation curves, weak lensing, and large-scale structure. The framework provides a unified emergent description of gravity and dark-sector phenomenology, with clear pathways for empirical validation. Files MS(5) -2.pdf Files (888.7 kB) Name Size Download all MS(5) -2.pdf md5:9b88535781abcd42fb1732b82221c808 888.7 kB Preview Download 37 Views 18 Downloads Show more details All versions This version Views Total views 37 37 Downloads Total downloads 18 18 Data volume Total data volume 17.8 MB 17.8 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Details DOI DOI Badge DOI 10.5281/zenodo.19520516 Markdown [](https://doi.org/10.5281/zenodo.19520516) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19520516.svg :target: https://doi.org/10.5281/zenodo.19520516 HTML <a href="https://doi.org/10.5281/zenodo.19520516"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19520516.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19520516.svg Target URL https://doi.org/10.5281/zenodo.19520516 Resource type Preprint Publisher Zenodo 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 11, 2026 Modified April 11, 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