{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:38:44Z","timestamp":1760146724215,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"LARSyS","award":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"],"award-info":[{"award-number":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"]}]},{"name":"FCT doctoral","award":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"],"award-info":[{"award-number":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"]}]},{"name":"La Caixa Foundation","award":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"],"award-info":[{"award-number":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"]}]},{"name":"Portuguese Foundation for Science and Technology","award":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"],"award-info":[{"award-number":["LA\/P\/0083\/2020","UIDP\/50009\/2020","UIDB\/50009\/2020","2021.08229.BD","LCF\/BQ\/PR22\/11920014","UIDB\/50026\/2020","UIDP\/50026\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy management, central to the Free Energy Principle, requires a process that temporarily shifts brain activity toward states of lower or higher entropy. Metastable synchronization is a process by which a system achieves entropy fluctuations by intermittently transitioning between states of collective order and disorder. Previous work has shown that collective oscillations, similar to those recorded from the brain, emerge spontaneously from weakly stable synchronization in critically coupled oscillator systems. However, direct evidence linking the formation of collective oscillations to entropy fluctuations is lacking. In this short communication, we demonstrate how the emergence of Metastable Oscillatory Modes (MOMs) is directly associated with a temporary reduction in entropy in the ongoing dynamics. We apply Shannon entropy to the distribution of eigenvalues of phase covariance over sliding time windows, capturing the temporal evolution of entropy at the level of the entire dynamical system. By demonstrating how the formation of MOMs impacts a system\u2019s entropy levels, we bridge theoretical works on the physics of coupled oscillators with the FEP framework, supporting the hypothesis that brain rhythms recorded experimentally are a signature of entropy management.<\/jats:p>","DOI":"10.3390\/e26121048","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T09:18:32Z","timestamp":1733217512000},"page":"1048","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Metastable Oscillatory Modes as a Signature of Entropy Management in the Brain"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6805-0034","authenticated-orcid":false,"given":"Marta","family":"Xavier","sequence":"first","affiliation":[{"name":"Institute for Systems and Robotics (ISR-Lisboa) and Department of Bioengineering, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal"},{"name":"Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Roc Boronat 138, 08018 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0743-0869","authenticated-orcid":false,"given":"Patr\u00edcia","family":"Figueiredo","sequence":"additional","affiliation":[{"name":"Institute for Systems and Robotics (ISR-Lisboa) and Department of Bioengineering, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8995-7583","authenticated-orcid":false,"given":"Gustavo","family":"Deco","sequence":"additional","affiliation":[{"name":"Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Roc Boronat 138, 08018 Barcelona, Spain"},{"name":"Instituci\u00f3 Catalana de la Recerca i Estudis Avan\u00e7ats (ICREA), Passeig Llu\u00eds Companys 23, 08010 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3461-6431","authenticated-orcid":false,"given":"Andrea I.","family":"Luppi","sequence":"additional","affiliation":[{"name":"Center for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford OX3 9BX, UK"},{"name":"Department of Psychiatry, University of Oxford, Oxford OX3 7JX, UK"},{"name":"St John\u2019s College, University of Cambridge, Cambridge CB2 1TP, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6715-0826","authenticated-orcid":false,"given":"Joana","family":"Cabral","sequence":"additional","affiliation":[{"name":"Center for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford OX3 9BX, UK"},{"name":"Life and Health Sciences Research Institute, University of Minho, 4710-057 Braga, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"key":"ref_1","first-page":"70","article-title":"A Free Energy Principle for the Brain","volume":"100","author":"Friston","year":"2006","journal-title":"J. Physiol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1038\/s42005-022-00950-y","article-title":"Metastable Oscillatory Modes Emerge from Synchronization in the Brain Spacetime Connectome","volume":"5","author":"Cabral","year":"2022","journal-title":"Commun. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hancock, F., Rosas, F.E., Zhang, M., Mediano, P.A.M., Luppi, A., Cabral, J., Deco, G., Kringelbach, M., Breakspear, M., and Scott Kelso, J.A. (2023). Metastability Demystified\u2014the Foundational Past, the Pragmatic Present, and the Potential Future. Preprint.","DOI":"10.20944\/preprints202307.1445.v1"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.pneurobio.2017.07.002","article-title":"Criticality in the Brain: A Synthesis of Neurobiology, Models and Cognition","volume":"158","author":"Cocchi","year":"2017","journal-title":"Prog. Neurobiol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"013108","DOI":"10.1063\/1.3305451","article-title":"Metastable Chimera States in Community-Structured Oscillator Networks","volume":"20","author":"Shanahan","year":"2010","journal-title":"Chaos"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"044101","DOI":"10.1103\/PhysRevLett.103.044101","article-title":"Large Coupled Oscillator Systems with Heterogeneous Interaction Delays","volume":"103","author":"Lee","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2753","DOI":"10.1103\/PhysRevLett.67.2753","article-title":"Collective Frequencies and Metastability in Networks of Limit-Cycle Oscillators with Time Delay","volume":"67","author":"Niebur","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"120236","DOI":"10.1016\/j.neuroimage.2023.120236","article-title":"Multi-Modal and Multi-Model Interrogation of Large-Scale Functional Brain Networks","volume":"277","author":"Timms","year":"2023","journal-title":"Neuroimage"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.neuroimage.2013.11.047","article-title":"Exploring Mechanisms of Spontaneous Functional Connectivity in MEG: How Delayed Network Interactions Lead to Structured Amplitude Envelopes of Band-Pass Filtered Oscillations","volume":"90","author":"Cabral","year":"2014","journal-title":"Neuroimage"},{"key":"ref_10","unstructured":"Buzsaki, G. (2006). Rhythms of the Brain, Oxford University Press."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kauffman, S.A. (1993). The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press.","DOI":"10.1093\/oso\/9780195079517.001.0001"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1038\/nrn2787","article-title":"The Free-Energy Principle: A Unified Brain Theory?","volume":"11","author":"Friston","year":"2010","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/BF01797193","article-title":"\u00dcber das Elektrenkephalogramm des Menschen","volume":"87","author":"Berger","year":"1929","journal-title":"Arch. F\u00fcr Psychiatr. Nervenkrankh."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1006\/nimg.1997.0259","article-title":"Transients, Metastability, and Neuronal Dynamics","volume":"5","author":"Friston","year":"1997","journal-title":"Neuroimage"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2987","DOI":"10.1038\/s41467-018-05316-z","article-title":"Spontaneous Cortical Activity Transiently Organizes into Frequency Specific Phase-Coupling Networks","volume":"9","author":"Vidaurre","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_16","unstructured":"Strogatz, S. (2004). Sync: The Emerging Science of Spontaneous Order, Penguin."},{"key":"ref_17","unstructured":"Strogatz, S.H. (2012). Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life, Hachette UK."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1504","DOI":"10.1038\/s41467-017-01190-3","article-title":"Oscillators That Sync and Swarm","volume":"8","author":"Hong","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Campbell, S.A. (2007). Time delays in neural systems. Handbook of Brain Connectivity, Springer.","DOI":"10.1007\/978-3-540-71512-2_2"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Lakshmanan, M., and Senthilkumar, D. (2010). Dynamics of Nonlinear Time-Delay Systems, Springer.","DOI":"10.1007\/978-3-642-14938-2"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Atay, F.M. (2010). Complex Time-Delay Systems: Theory and Applications, Springer. [1st ed.].","DOI":"10.1007\/978-3-642-02329-3"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Biswas, D., and Banerjee, T. (2017). Time-Delayed Chaotic Dynamical Systems: From Theory to Electronic Experiment, Springer.","DOI":"10.1007\/978-3-319-70993-2"},{"key":"ref_23","first-page":"20180389","article-title":"Nonlinear dynamics of delay systems: An overview","volume":"377","author":"Otto","year":"2019","journal-title":"Philos. Trans. A Math. Phys. Eng. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1006\/nimg.2001.0978","article-title":"Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain","volume":"15","author":"Landeau","year":"2002","journal-title":"Neuroimage"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"144101","DOI":"10.1103\/PhysRevLett.92.144101","article-title":"Delays, connection topology, and synchronization of coupled chaotic maps","volume":"92","author":"Atay","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","unstructured":"Jolliffe, I.T. (2002). Principal Component Analysis for Special Types of Data. Principal Component Analysis, Springer."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/0013-4694(91)90138-T","article-title":"Quantification of EEG irregularity by use of the entropy of the power spectrum","volume":"79","author":"Inouye","year":"1991","journal-title":"Electroencephalogr. Clin. Neurophysiol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bengtsson, I., and Zyczkowski, K. (2006). Geometry of Quantum States: An Introduction to Quantum Entanglement, Cambridge University Press (CUP).","DOI":"10.1017\/CBO9780511535048"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1103\/PhysRevLett.82.648","article-title":"Time Delay in the Kuramoto Model of Coupled Oscillators","volume":"82","author":"Strogatz","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"043131","DOI":"10.1063\/1.4766592","article-title":"Metastability and chimera states in modular delay and pulse-coupled oscillator networks","volume":"22","author":"Wildie","year":"2012","journal-title":"Chaos"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Caprioglio, E., and Berthouze, L. (2024). Emergence of metastability in frustrated oscillatory networks: The key role of hierarchical modularity. Front. Netw. Physiol., 4.","DOI":"10.3389\/fnetp.2024.1436046"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hizanidis, J., Kouvaris, N.E., Zamora-L\u00f3pez, G., D\u00edaz-Guilera, A., and Antonopoulos, C.G. (2016). Chimera-like States in Modular Neural Networks. Sci. Rep., 6.","DOI":"10.1038\/srep19845"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.neuroimage.2013.05.041","article-title":"The WU-Minn Human Connectome Project: An overview","volume":"80","author":"Smith","year":"2013","journal-title":"Neuroimage"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.neuroimage.2018.08.068","article-title":"Lead-DBS v2: Towards a comprehensive pipeline for deep brain stimulation imaging","volume":"184","author":"Horn","year":"2019","journal-title":"Neuroimage"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/12\/1048\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:46:02Z","timestamp":1760114762000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/12\/1048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["e26121048"],"URL":"https:\/\/doi.org\/10.3390\/e26121048","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,12,3]]}}}