{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T17:10:10Z","timestamp":1779210610994,"version":"3.51.4"},"reference-count":61,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T00:00:00Z","timestamp":1715212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12175002"],"award-info":[{"award-number":["12175002"]}]},{"name":"National Natural Science Foundation of China","award":["11705004"],"award-info":[{"award-number":["11705004"]}]},{"name":"National Natural Science Foundation of China","award":["12381240288"],"award-info":[{"award-number":["12381240288"]}]},{"name":"National Natural Science Foundation of China","award":["1222020"],"award-info":[{"award-number":["1222020"]}]},{"name":"National Natural Science Foundation of China","award":["BPHR202203034"],"award-info":[{"award-number":["BPHR202203034"]}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"publisher","award":["12175002"],"award-info":[{"award-number":["12175002"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"publisher","award":["11705004"],"award-info":[{"award-number":["11705004"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"publisher","award":["12381240288"],"award-info":[{"award-number":["12381240288"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"publisher","award":["1222020"],"award-info":[{"award-number":["1222020"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Natural Science Foundation of Beijing","doi-asserted-by":"publisher","award":["BPHR202203034"],"award-info":[{"award-number":["BPHR202203034"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project of Cultivation for Young top-notch Talents of Beijing Municipal Institutions","award":["12175002"],"award-info":[{"award-number":["12175002"]}]},{"name":"Project of Cultivation for Young top-notch Talents of Beijing Municipal Institutions","award":["11705004"],"award-info":[{"award-number":["11705004"]}]},{"name":"Project of Cultivation for Young top-notch Talents of Beijing Municipal Institutions","award":["12381240288"],"award-info":[{"award-number":["12381240288"]}]},{"name":"Project of Cultivation for Young top-notch Talents of Beijing Municipal Institutions","award":["1222020"],"award-info":[{"award-number":["1222020"]}]},{"name":"Project of Cultivation for Young top-notch Talents of Beijing Municipal Institutions","award":["BPHR202203034"],"award-info":[{"award-number":["BPHR202203034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We reveal the continuous change of information dynamics patterns in anyonic-PT symmetric systems that originates from the continuity of anyonic-PT symmetry. We find there are three information dynamics patterns for anyonic-PT symmetric systems: damped oscillations with an overall decrease (increase) and asymptotically stable damped oscillations, which are three-fold degenerate and are distorted using the Hermitian quantum R\u00e9nyi entropy or distinguishability. It is the normalization of the non-unitary evolved density matrix that causes the degeneracy and distortion. We give a justification for non-Hermitian quantum R\u00e9nyi entropy being negative. By exploring the mathematics and physical meaning of the negative entropy in open quantum systems, we connect negative non-Hermitian quantum R\u00e9nyi entropy and negative quantum conditional entropy, paving the way to rigorously investigate negative entropy in open quantum systems.<\/jats:p>","DOI":"10.3390\/sym16050584","type":"journal-article","created":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T05:16:45Z","timestamp":1715231805000},"page":"584","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Non-Hermitian Quantum R\u00e9nyi Entropy Dynamics in Anyonic-PT Symmetric Systems"],"prefix":"10.3390","volume":"16","author":[{"given":"Zhihang","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Physics, College of Science, North China University of Technology, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8942-6651","authenticated-orcid":false,"given":"Chao","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Science, North China University of Technology, Beijing 100144, China"},{"name":"School of Energy Storage Science and Engineering, North China University of Technology, Beijing 100144, China"},{"name":"Beijing Laboratory of New Energy Storage Technology, Beijing 100144, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Breuer, H.P., and Petruccione, F. 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