{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,9]],"date-time":"2026-08-09T04:40:52Z","timestamp":1786250452348,"version":"3.56.0"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T00:00:00Z","timestamp":1616025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tiny Blue Dot Foundation","award":["UW 133AAG3451"],"award-info":[{"award-number":["UW 133AAG3451"]}]},{"DOI":"10.13039\/501100011730","name":"Templeton World Charity Foundation","doi-asserted-by":"publisher","award":["TWCF0216"],"award-info":[{"award-number":["TWCF0216"]}],"id":[{"id":"10.13039\/501100011730","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) that captures three postulates of IIT\u2014existence, intrinsicality and information\u2014and is unique. Here we show that the new measure also satisfies the remaining postulates of IIT\u2014integration and exclusion\u2014and create the framework that identifies maximally irreducible mechanisms. These mechanisms can then form maximally irreducible systems, which in turn will specify the physical substrate of conscious experience.<\/jats:p>","DOI":"10.3390\/e23030362","type":"journal-article","created":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T11:41:06Z","timestamp":1616067666000},"page":"362","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Mechanism Integrated Information"],"prefix":"10.3390","volume":"23","author":[{"given":"Leonardo S.","family":"Barbosa","sequence":"first","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin-Madison, Madison, WI 53719, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Marshall","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin-Madison, Madison, WI 53719, USA"},{"name":"Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1000-9917","authenticated-orcid":false,"given":"Larissa","family":"Albantakis","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin-Madison, Madison, WI 53719, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giulio","family":"Tononi","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin-Madison, Madison, WI 53719, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Overgaard, M., Mogensen, J., and Kirkeby-Hinrup, A. (2020). Integrated information theory. Beyond Neural Correlates of Consciousness, Routledge.","DOI":"10.4324\/9781315205267"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1038\/nrn.2016.44","article-title":"Integrated information theory: From consciousness to its physical substrate","volume":"17","author":"Tononi","year":"2016","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Oizumi, M., Albantakis, L., and Tononi, G. (2014). From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3. 0. PLoS Comput Biol, 10.","DOI":"10.1371\/journal.pcbi.1003588"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Balduzzi, D., and Tononi, G. (2008). Integrated information in discrete dynamical systems: Motivation and theoretical framework. PLoS Comput. Biol., 4.","DOI":"10.1371\/journal.pcbi.1000091"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-020-75943-4","article-title":"A measure for intrinsic information","volume":"10","author":"Barbosa","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Tononi, G. (2017). The Integrated Information Theory of Consciousness. The Blackwell Companion to Consciousness, John Wiley & Sons, Ltd.","DOI":"10.1002\/9781119132363.ch17"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"459","DOI":"10.3390\/e21050459","article-title":"What caused what? A quantitative account of actual causation using dynamical causal networks","volume":"21","author":"Albantakis","year":"2019","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"216","DOI":"10.2307\/25470707","article-title":"Consciousness as integrated information: A provisional manifesto","volume":"215","author":"Tononi","year":"2008","journal-title":"Biol. Bull."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Marshall, W., Albantakis, L., and Tononi, G. (2018). Black-boxing and cause-effect power. PLoS Comput. Biol., 14.","DOI":"10.1371\/journal.pcbi.1006114"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.3390\/e21121160","article-title":"Why Does Space Feel the Way it Does? Towards a Principled Account of Spatial Experience","volume":"21","author":"Haun","year":"2019","journal-title":"Entropy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5472","DOI":"10.3390\/e17085472","article-title":"The Intrinsic Cause-Effect Power of Discrete Dynamical Systems\u2014From Elementary Cellular Automata to Adapting Animats","volume":"17","author":"Albantakis","year":"2015","journal-title":"Entropy"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Albantakis, L., and Tononi, G. (2019). Causal Composition: Structural Differences among Dynamically Equivalent Systems. Entropy, 21.","DOI":"10.3390\/e21100989"},{"key":"ref_13","first-page":"926","article-title":"Integrated Information and State Differentiation","volume":"7","author":"Marshall","year":"2016","journal-title":"Conscious. Res."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gomez, J.D., Mayner, W.G.P., Beheler-Amass, M., Tononi, G., and Albantakis, L. (2021). Computing Integrated Information (\u03a6) in Discrete Dynamical Systems with Multi-Valued Elements. Entropy, 23.","DOI":"10.3390\/e23010006"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"261","DOI":"10.3390\/e10030261","article-title":"Axiomatic Characterizations of Information Measures","volume":"10","year":"2008","journal-title":"Entropy"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Tononi, G. (2004). An information integration theory of consciousness. BMC Neurosci., 5.","DOI":"10.1186\/1471-2202-5-42"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"405","DOI":"10.3390\/e21040405","article-title":"Exclusion and Underdetermined Qualia","volume":"21","author":"Kyumin","year":"2019","journal-title":"Entropy"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Pearl, J. (2009). Causality, Cambridge University Press.","DOI":"10.1017\/CBO9780511803161"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2324","DOI":"10.1214\/13-AOS1145","article-title":"Quantifying causal influences","volume":"41","author":"Janzing","year":"2013","journal-title":"Ann. Stat."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ebanks, B., Sahoo, P., and Sander, W. (1998). Characterizations of Information Measures, World Scientific.","DOI":"10.1142\/9789812817167"},{"key":"ref_21","unstructured":"Krantz, S.G., and Parks, H.R. (2002). A Primer of Real Analytic Functions, Birkh\u00e4user Advanced Texts Basler Lehrb\u00fccher; Birkh\u00e4user. [2nd ed.]."},{"key":"ref_22","unstructured":"Acz\u00e9l, J. (2006). Lectures on Functional Equations and Their Applications, Dover Publications."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/3\/362\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:37:42Z","timestamp":1760161062000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/3\/362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,18]]},"references-count":22,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["e23030362"],"URL":"https:\/\/doi.org\/10.3390\/e23030362","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,18]]}}}