{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T07:05:48Z","timestamp":1792566348950,"version":"4.5.0"},"reference-count":87,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T00:00:00Z","timestamp":1631836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-19-1-2556"],"award-info":[{"award-number":["N00014-19-1-2556"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001866","name":"Fonds National de la Recherche Luxembourg","doi-asserted-by":"publisher","award":["13568875"],"award-info":[{"award-number":["13568875"]}],"id":[{"id":"10.13039\/501100001866","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004440","name":"Wellcome","doi-asserted-by":"publisher","award":["088130\/Z\/09\/Z"],"award-info":[{"award-number":["088130\/Z\/09\/Z"]}],"id":[{"id":"10.13039\/100004440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this treatment of random dynamical systems, we consider the existence\u2014and identification\u2014of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions\u2014and the functional form of the underlying densities\u2014have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition\u2014and polynomial expansions\u2014to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified\u2014using the accompanying Hessian\u2014to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology.<\/jats:p>","DOI":"10.3390\/e23091220","type":"journal-article","created":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T21:23:29Z","timestamp":1631913809000},"page":"1220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":50,"title":["Stochastic Chaos and Markov Blankets"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-8909","authenticated-orcid":false,"given":"Karl","family":"Friston","sequence":"first","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Conor","family":"Heins","sequence":"additional","affiliation":[{"name":"Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78457 Konstanz, Germany"},{"name":"Centre for the Advanced Study of Collective Behaviour, 78457 Konstanz, Germany"},{"name":"Department of Biology, University of Konstanz, 78457 Konstanz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Ueltzh\u00f6ffer","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London WC1N 3AR, UK"},{"name":"Department of General Psychiatry, Centre of Psychosocial Medicine, Heidelberg University, Vo\u00dfstra\u00dfe 2, 69115 Heidelberg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0126-4588","authenticated-orcid":false,"given":"Lancelot","family":"Da Costa","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London WC1N 3AR, UK"},{"name":"Department of Mathematics, Imperial College London, London SW7 2AZ, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5108-5743","authenticated-orcid":false,"given":"Thomas","family":"Parr","sequence":"additional","affiliation":[{"name":"Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"061106","DOI":"10.1103\/PhysRevE.84.061106","article-title":"Nonequilibrium steady state of a stochastic system driven by a nonlinear drift force","volume":"84","author":"Kwon","year":"2011","journal-title":"Phys. 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