{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:51:45Z","timestamp":1760057505129,"version":"build-2065373602"},"reference-count":126,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T00:00:00Z","timestamp":1739404800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MUR project PRIN2022 \u201cEnantioSelex\u201d","award":["2022P9F79R"],"award-info":[{"award-number":["2022P9F79R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other approaches, briefly sketched in the text, have advocated the need to deal with both quantum and classical dynamic variables when studying the brain. At variance with these other frameworks, the manuscript\u2019s formalism allows us to explicitly treat the classical dynamical variables. The theory must be dissipative not because of formal requirements but because brain processes appear to be dissipative at the molecular, physiological, and high functional levels. We discuss theoretically that using Brownian dynamics or the Nos\u00e8-Hoover-Chain thermostat to perform computer simulations provides an effective way to introduce an arrow of time for open quantum systems in a classical environment. In the future, We plan to study classical models of neurons and astrocytes, as well as their networks, coupled to quantum dynamical variables describing, e.g., nuclear and electron spins, HOMO and LUMO orbitals of phenyl and indole rings, ion channels, and tunneling protons.<\/jats:p>","DOI":"10.3390\/sym17020285","type":"journal-article","created":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T04:03:35Z","timestamp":1739419415000},"page":"285","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Time-Irreversible Quantum-Classical Dynamics of Molecular Models in the Brain"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3954-0445","authenticated-orcid":false,"given":"Alessandro","family":"Sergi","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit\u00e0 degli Studi di Messina, Viale F. Stagno d\u2019Alcontres 31, 98166 Messina, Italy"},{"name":"Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3367-0129","authenticated-orcid":false,"given":"Antonino","family":"Messina","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica ed Informatica, Universit\u00e0 di Palermo, Via Archirafi 34, 90123 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5823-9749","authenticated-orcid":false,"given":"Rosalba","family":"Saija","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit\u00e0 degli Studi di Messina, Viale F. Stagno d\u2019Alcontres 31, 98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9488-2021","authenticated-orcid":false,"given":"Gabriella","family":"Martino","sequence":"additional","affiliation":[{"name":"Dipartimento di Medicina e Clinica Sperimentale, Universit\u00e0 degli Studi di Messina, Via Consolare Valeria, 98125 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2417-0998","authenticated-orcid":false,"given":"Maria Teresa","family":"Caccamo","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit\u00e0 degli Studi di Messina, Viale F. Stagno d\u2019Alcontres 31, 98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min-Fang","family":"Kuo","sequence":"additional","affiliation":[{"name":"Department Psychology and Neurosciences, Leibniz Research Centre for Working Environment and Human Factors, 44139 Dortmund, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael A.","family":"Nitsche","sequence":"additional","affiliation":[{"name":"Department Psychology and Neurosciences, Leibniz Research Centre for Working Environment and Human Factors, 44139 Dortmund, Germany"},{"name":"German Center for Mental Health (DZPG), 44787 Bochum, Germany"},{"name":"University Clinic of Psychiatry and Psychotherapy, Protestant Hospital of Bethel Foundation, University Hospital OWL, Bielefeld University, 33602 Bielefeld, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Abbot, D., Davies, P.C.W., and Pati, A.K. 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