{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:08:44Z","timestamp":1773148124363,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2012,7,12]],"date-time":"2012-07-12T00:00:00Z","timestamp":1342051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov\u2013Sinai (dynamical) entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following, we establish a similar relation between the Connes\u2013Narnhofer\u2013Thirring quantum dynamical entropy for the shift on quantum spin chains and the G\u00e1cs algorithmic entropy. We further provide, for the same system, a weaker linkage between the latter algorithmic complexity and a different quantum dynamical entropy proposed by Alicki and Fannes.<\/jats:p>","DOI":"10.3390\/e14071259","type":"journal-article","created":{"date-parts":[[2012,7,13]],"date-time":"2012-07-13T05:28:49Z","timestamp":1342157329000},"page":"1259-1273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Quantum Dynamical Entropies and G\u00e1cs Algorithmic Entropy"],"prefix":"10.3390","volume":"14","author":[{"given":"Fabio","family":"Benatti","sequence":"first","affiliation":[{"name":"Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy"},{"name":"INFN, Trieste, Strada Costiera 11, I-34151 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cornfeld, I.P., Fomin, S.V., and Sinai, Y.G. 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