{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:50:43Z","timestamp":1760143843633,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009566","name":"Templeton World Charity Foundation Power of Information Fellowship","doi-asserted-by":"publisher","award":["FQXi-RFP-IPW-1902","W911NF-21-1-0048","W911NF-18-1-0028"],"award-info":[{"award-number":["FQXi-RFP-IPW-1902","W911NF-21-1-0048","W911NF-18-1-0028"]}],"id":[{"id":"10.13039\/100009566","id-type":"DOI","asserted-by":"publisher"}]},{"name":"U.S. Army Research Laboratory and the U.S. Army Research Office","award":["FQXi-RFP-IPW-1902","W911NF-21-1-0048","W911NF-18-1-0028"],"award-info":[{"award-number":["FQXi-RFP-IPW-1902","W911NF-21-1-0048","W911NF-18-1-0028"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally-suitable, possibilities. Following Jaynes\u2019 information-theoretic perspective, this can be framed as an inference problem. We propose the Maximum Geometric Quantum Entropy Principle to exploit the notions of Quantum Information Dimension and Geometric Quantum Entropy. These allow us to quantify the entropy of fully arbitrary ensembles and select the one that maximizes it. After formulating the principle mathematically, we give the analytical solution to the maximization problem in a number of cases and discuss the physical mechanism behind the emergence of such maximum entropy ensembles.<\/jats:p>","DOI":"10.3390\/e26030225","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T07:36:21Z","timestamp":1709278581000},"page":"225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Maximum Geometric Quantum Entropy"],"prefix":"10.3390","volume":"26","author":[{"given":"Fabio","family":"Anza","sequence":"first","affiliation":[{"name":"Department of Mathematics Informatics and Geoscience, University of Trieste, Via Alfonso Valerio 2, 34127 Trieste, Italy"},{"name":"Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4466-5410","authenticated-orcid":false,"given":"James P.","family":"Crutchfield","sequence":"additional","affiliation":[{"name":"Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref_1","unstructured":"Pathria, R.K., and Beale, P.D. 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