{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:35:21Z","timestamp":1759970121231,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research, Development and Innovation Office (Hungary) Frontline Research Excellence Program","award":["KKP133827"],"award-info":[{"award-number":["KKP133827"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We show that the minimum entropy production in near-reversible quantum state transport along a path is a simple function of the path length measured according to the Fisher\u2013KMB metrics. Hence, for the sharp values of path lengths, also called statistical lengths, we obtain the operational meaning to quantify the residual irreversibility in near-reversible state transport. In the classical limit, the Bhattacharyya fidelity is found to have a sharp operational meaning after eighty years.<\/jats:p>","DOI":"10.3390\/e27010042","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T05:06:34Z","timestamp":1736226394000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Operational Meaning of Classical Fidelity and Path Length in Kubo\u2013Mori\u2013Bogoliubov Fisher Geometry"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4722-3220","authenticated-orcid":false,"given":"Lajos","family":"Di\u00f3si","sequence":"first","affiliation":[{"name":"Wigner Research Center for Physics, P.O. Box 49, H-1525 Budapest 114, Hungary"},{"name":"Department of Physics of Complex Systems, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter stny. 1\/A, H-1117 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"key":"ref_1","first-page":"99","article-title":"On a measure of divergence between two statistical populations defined by their probability distribution","volume":"35","author":"Bhattacharyya","year":"1943","journal-title":"Bull. Calcutta Math. Soc."},{"key":"ref_2","first-page":"199","article-title":"An extension of Kakutani\u2019s theorem on infinite product measures to the tensor product of semifinite w*-algebras","volume":"135","author":"Bures","year":"1969","journal-title":"Trans. Am. Math. 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