{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T16:22:40Z","timestamp":1787674960641,"version":"build-2784847793"},"reference-count":124,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100004440","name":"Wellcome Trust","doi-asserted-by":"publisher","award":["226793\/Z\/22\/Z"],"award-info":[{"award-number":["226793\/Z\/22\/Z"]}],"id":[{"id":"10.13039\/100004440","id-type":"DOI","asserted-by":"publisher"}]},{"award":["226793\/Z\/22\/Z"],"award-info":[{"award-number":["226793\/Z\/22\/Z"]}],"id":[{"id":"https:\/\/ror.org\/029chgv08","id-type":"ROR","asserted-by":"publisher"}]},{"name":"K. Lisa Yang Integrative Computational Neuroscience (ICoN) Center of the Yang-Tan Collective at MIT"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We apply the free energy principle to free markets by treating the Market as a random dynamical system with an attracting set, i.e., some characteristic states. This licenses a normal form for stochastic dynamics that inherits from the Helmholtz\u2013Hodge decomposition. Equipped with this functional form\u2014and a suitable parameterization\u2014one can create a generative model of fluctuations in the value of assets and accompanying indicator variables. This affords the opportunity for prospective (ex ante) prediction, scenario modelling and forecasting that could, in principle, be applied to any complex dynamical system exhibiting stochastic chaos. Here, we illustrate the application to portfolio management\u2014in the context of financial services\u2014and use the (posterior) predictive densities over future paths to evaluate the expected free energy that underwrites active inference. In this application, active inference reduces to risk-sensitive control, which can be used to model the optimal decision-making of an agent or investor. In this setting, an investor is characterized by their prior preferences for a high rate of return under drawdown constraints. Using numerical studies and historical financial data, we quantify the improvement in portfolio management, relative to baseline policies.<\/jats:p>","DOI":"10.3390\/e28090956","type":"journal-article","created":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T15:55:06Z","timestamp":1787673306000},"page":"956","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Free Energy Principle and Free Markets"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-8909","authenticated-orcid":false,"given":"Karl","family":"Friston","sequence":"first","affiliation":[{"name":"Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johan","family":"Medrano","sequence":"additional","affiliation":[{"name":"Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK"},{"name":"K. Lisa Yang ICoN Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tim","family":"Verbelen","sequence":"additional","affiliation":[{"name":"VERSES, Los Angeles, CA 90016, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2210","DOI":"10.1093\/brain\/awu133","article-title":"On the nature of seizure dynamics","volume":"137","author":"Jirsa","year":"2014","journal-title":"Brain"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1038\/s41467-018-02973-y","article-title":"Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy","volume":"9","author":"Proix","year":"2018","journal-title":"Nat. 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