{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T05:41:36Z","timestamp":1771998096074,"version":"3.50.1"},"reference-count":104,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,11]],"date-time":"2023-12-11T00:00:00Z","timestamp":1702252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We discuss the asymmetries of dynamical origin that are relevant to functional brain activity. The brain is permanently open to its environment, and its dissipative dynamics is characterized indeed by the asymmetries under time translation transformations and time-reversal transformations, which manifest themselves in the irreversible \u201carrow of time\u201d. Another asymmetry of dynamical origin arises from the breakdown of the rotational symmetry of molecular electric dipoles, triggered by incoming stimuli, which manifests in long-range dipole-dipole correlations favoring neuronal correlations. In the dissipative model, neurons, glial cells, and other biological components are classical structures. The dipole vibrational fields are quantum variables. We review the quantum field theory model of the brain proposed by Ricciardi and Umezawa and its subsequent extension to dissipative dynamics. We then show that Bayes\u2019 theorem in probability theory is intrinsic to the structure of the brain states and discuss its strict relation with entanglement phenomena and free energy minimization. The brain estimates the action with a higher Bayes probability to be taken to produce the aimed effect. Bayes\u2019 rule provides the formal basis of the intentionality in brain activity, which we also discuss in relation to mind and consciousness.<\/jats:p>","DOI":"10.3390\/sym15122184","type":"journal-article","created":{"date-parts":[[2023,12,11]],"date-time":"2023-12-11T06:56:00Z","timestamp":1702277760000},"page":"2184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Dynamical Asymmetries, the Bayes\u2019 Theorem, Entanglement, and Intentionality in the Brain Functional Activity"],"prefix":"10.3390","volume":"15","author":[{"given":"David","family":"Bernal-Casas","sequence":"first","affiliation":[{"name":"Department of Genetics, Microbiology and Statistics, Faculty of Biology, University of Barcelona, 08028 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5710-7904","authenticated-orcid":false,"given":"Giuseppe","family":"Vitiello","sequence":"additional","affiliation":[{"name":"Department of Physics \u201cE.R. Caianiello\u201d, University of Salerno, 84084 Fisciano, Salerno, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/BF00292170","article-title":"Brain and physics of many-body problems","volume":"4","author":"Ricciardi","year":"1967","journal-title":"Kybernetik"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Globus, G.G., Pribram, K.H., and Vitiello, G. (2004). Brain and Being. At the Boundary between Science, Philosophy, Language and Arts, John Benjamins Publ. Co.","DOI":"10.1075\/aicr.58"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/0022-5193(78)90327-2","article-title":"On the stability and non-local properties of memory","volume":"71","author":"Stuart","year":"1978","journal-title":"J. Theor. 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