{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T17:09:27Z","timestamp":1779210567283,"version":"3.51.4"},"reference-count":81,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T00:00:00Z","timestamp":1667088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12175002"],"award-info":[{"award-number":["12175002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11705004"],"award-info":[{"award-number":["11705004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["1222020"],"award-info":[{"award-number":["1222020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","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":"Beijing Natural Science Foundation","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":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["1222020"],"award-info":[{"award-number":["1222020"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NCUT Talents Project","award":["12175002"],"award-info":[{"award-number":["12175002"]}]},{"name":"NCUT Talents Project","award":["11705004"],"award-info":[{"award-number":["11705004"]}]},{"name":"NCUT Talents Project","award":["1222020"],"award-info":[{"award-number":["1222020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>From their conception to present times, different concepts and definitions of entropy take key roles in a variety of areas from thermodynamics to information science, and they can be applied to both classical and quantum systems. Among them is the R\u00e9nyi entropy. It is able to characterize various properties of classical information with a unified concise form. We focus on the quantum counterpart, which unifies the von Neumann entropy, max- and min-entropy, collision entropy, etc. It can only be directly applied to Hermitian systems because it usually requires that the density matrices is normalized. For a non-Hermitian system, the evolved density matrix may not be normalized; i.e., the trace can be larger or less than one as the time evolution. However, it is not well-defined for the R\u00e9nyi entropy with a non-normalized probability distribution relevant to the density matrix of a non-Hermitian system, especially when the trace of the non-normalized density matrix is larger than one. In this work, we investigate how to describe the R\u00e9nyi entropy for non-Hermitian systems more appropriately. We obtain a concisely and generalized form of \u03b1-R\u00e9nyi entropy, which we extend the unified order-\u03b1 from finite positive real numbers to zero and infinity. Our generalized \u03b1-R\u00e9nyi entropy can be directly calculated using both of the normalized and non-normalized density matrices so that it is able to describe non-Hermitian entropy dynamics. We illustrate the necessity of our generalization by showing the differences between ours and the conventional R\u00e9nyi entropy for non-Hermitian detuning two-level systems.<\/jats:p>","DOI":"10.3390\/e24111563","type":"journal-article","created":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T04:57:34Z","timestamp":1667105854000},"page":"1563","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Non-Hermitian Generalization of R\u00e9nyi Entropy"],"prefix":"10.3390","volume":"24","author":[{"given":"Daili","family":"Li","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"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Greven, A., Keller, G., and Warnecke, G. 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