{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T20:04:25Z","timestamp":1773950665911,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T00:00:00Z","timestamp":1721779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>When describing Active Inference Agents (AIAs), the term \u201cenergy\u201d can have two distinct meanings. One is the energy that is utilized by the AIA (e.g., electrical energy or chemical energy). The second meaning is so-called Variational Free Energy (VFE), a statistical quantity which provides an upper bound on surprisal. In this paper, we develop an account of the former quantity\u2014the Thermodynamic Free Energy (TFE)\u2014and its relationship with the latter. We highlight the necessary tradeoffs between these two in a generic, quantum information-theoretic formulation, and the macroscopic consequences of those tradeoffs for the ways that organisms approach their environments. By making this tradeoff explicit, we provide a theoretical basis for the different metabolic strategies that organisms from plants to predators use to survive.<\/jats:p>","DOI":"10.3390\/e26080622","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T14:55:47Z","timestamp":1721832947000},"page":"622","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Making the Thermodynamic Cost of Active Inference Explicit"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4812-0744","authenticated-orcid":false,"given":"Chris","family":"Fields","sequence":"first","affiliation":[{"name":"Independent Researcher, 11160 Caunes Minervois, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1572-8136","authenticated-orcid":false,"given":"Adam","family":"Goldstein","sequence":"additional","affiliation":[{"name":"Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford OX1 3PT, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2282-1438","authenticated-orcid":false,"given":"Lars","family":"Sandved-Smith","sequence":"additional","affiliation":[{"name":"Monash Centre for Consciousness and Contemplative Studies, Monash University, Melbourne 3168, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,24]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"20130475","DOI":"10.1098\/rsif.2013.0475","article-title":"Life as we know it","volume":"10","author":"Friston","year":"2013","journal-title":"J. R. Soc. Interface"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/NECO_a_00912","article-title":"Active inference: A process theory","volume":"29","author":"Friston","year":"2017","journal-title":"Neural Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.plrev.2017.09.001","article-title":"Answering Schrodinger\u2019s question: A free-energy formulation","volume":"24","author":"Ramstead","year":"2018","journal-title":"Phys. Life Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.plrev.2018.12.002","article-title":"Variational ecology and the physics of sentient systems","volume":"31","author":"Ramstead","year":"2019","journal-title":"Phys. Life Rev."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ororbia, A., and Friston, K. (2023). Mortal computation: A foundation for biomimetic intelligence. arXiv.","DOI":"10.31219\/osf.io\/epqkg"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Friston, K., Thornton, C., and Clark, A. (2012). Free-energy minimization and the dark-room problem. Front. Psychol., 3.","DOI":"10.3389\/fpsyg.2012.00130"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Sengupta, S., Stemmler, M.B., and Friston, K.J. (2013). Information and efficiency in the nervous system\u2013A synthesis. PLoS Comp. Biol., 9.","DOI":"10.1371\/journal.pcbi.1003157"},{"key":"ref_9","unstructured":"Friston, K.J. (2019). A free energy principle for a particular physics. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"20220029","DOI":"10.1098\/rsfs.2022.0029","article-title":"On Bayesian mechanics: A physics of and by beliefs","volume":"13","author":"Ramstead","year":"2022","journal-title":"Interface Focus"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.plrev.2023.08.016","article-title":"Path integrals, particular kinds, and strange things","volume":"47","author":"Friston","year":"2023","journal-title":"Phys. Life Rev."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Fields, C., and Glazebrook, J.F. (2020). Representing measurement as a thermodynamic symmetry breaking. Symmetry, 12.","DOI":"10.3390\/sym12050810"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.pbiomolbio.2022.05.006","article-title":"A free energy principle for generic quantum systems","volume":"173","author":"Fields","year":"2022","journal-title":"Prog. Biophys. Mol. Biol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"102632","DOI":"10.1016\/j.jmp.2021.102632","article-title":"A step-by-step tutorial on active inference and its application to empirical data","volume":"107","author":"Smith","year":"2022","journal-title":"J. Math. Psychol."},{"key":"ref_15","unstructured":"Clausius, R. (1867). The Mechanical Theory of Heat\u2013with Its Applications to the Steam Engine and to Physical Properties of Bodies, John van Voorst."},{"key":"ref_16","first-page":"373","article-title":"On the relationship between the second fundamental theorem of the mechanical theory of heat and probability calculations regarding the conditions for thermal equilibrium","volume":"LXXVI","author":"Boltzmann","year":"1877","journal-title":"Sitz. Kaiserlichen Akad. Wissenschaften Mathematisch-Naturwissen Classe Abt. II"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Irreversibility and heat generation in the computing process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM J. Res. Dev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/S0378-4371(98)00513-5","article-title":"Information is a physical entity","volume":"263","author":"Landauer","year":"1999","journal-title":"Physia A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"20140182","DOI":"10.1098\/rspa.2014.0182","article-title":"When does a physical system compute?","volume":"470","author":"Horsman","year":"2014","journal-title":"Proc. R. Soc. A"},{"key":"ref_20","unstructured":"Cummins, R. (1983). The Nature of Psychological Explanation, MIT Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1080\/09528138908953699","article-title":"Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems","volume":"1","author":"Fields","year":"1989","journal-title":"J. Expt. Theor. Artif. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2307\/2102968","article-title":"The semantic conception of truth and the foundations of semantics","volume":"4","author":"Tarski","year":"1944","journal-title":"Philos. Phenomenol. Res."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Fields, C. (2024). The free energy principle induces compartmentalization. Biochem. Biophys. Res. Commun., 723.","DOI":"10.1016\/j.bbrc.2024.150070"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/TMBMC.2023.3272150","article-title":"Control flow in active inference systems, Part I: Classical and quantum formulations of active inference","volume":"9","author":"Fields","year":"2023","journal-title":"IEEE Trans. Mol. Biol. Multi-Scale Commun."},{"key":"ref_25","unstructured":"Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1103\/RevModPhys.74.825","article-title":"The holographic principle","volume":"74","author":"Bousso","year":"2022","journal-title":"Rev. Mod. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"72","DOI":"10.12743\/quanta.v11i1.206","article-title":"The physical meaning of the Holographic Principle","volume":"11","author":"Fields","year":"2022","journal-title":"Quanta"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1103\/PhysRevD.30.368","article-title":"Quantum frames of reference","volume":"30","author":"Aharonov","year":"1984","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1103\/RevModPhys.79.555","article-title":"Reference frames, superselection rules, and quantum information","volume":"79","author":"Bartlett","year":"2007","journal-title":"Rev. Mod. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"202200104","DOI":"10.1002\/prop.202200104","article-title":"Sequential measurements, topological quantum field theories, and topological quantum neural networks","volume":"70","author":"Fields","year":"2022","journal-title":"Fortschr. Phys."},{"key":"ref_31","unstructured":"Ad\u00e1mek, J., Herrlich, H., and Strecker, G.E. (1990). Abstract and Concrete Categories: The Joy of Cats, Wiley. Available online: http:\/\/katmat.math.uni-bremen.de\/acc."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Fields, C., Glazebrook, J.F., and Levin, M. (2024). Principled limitations on self-representation for generic physical systems. Entropy, 26.","DOI":"10.3390\/e26030194"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/BF02084158","article-title":"The thermodynamics of computation","volume":"21","author":"Bennett","year":"1982","journal-title":"Int. J. Theor. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nphys3230","article-title":"Thermodynamics of information","volume":"11","author":"Parrondo","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Fields, C., and Levin, M. (2021). Metabolic limits on classical information processing by biological cells. Biosystems, 209.","DOI":"10.1016\/j.biosystems.2021.104513"},{"key":"ref_36","unstructured":"Bateson, G. (1972). Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution, and Epistemology, Jason Aronson."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/s10441-019-09375-7","article-title":"On the variety of cognitive temperatures and their symmetry-breaking dynamics","volume":"68","author":"Wallace","year":"2020","journal-title":"Acta Biotheor."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"215","DOI":"10.3389\/fnhum.2010.00215","article-title":"Attention, uncertainty, and free-energy","volume":"4","author":"Feldman","year":"2010","journal-title":"Front. Hum. Neurosci."},{"key":"ref_39","first-page":"niab018","article-title":"Towards a computational phenomenology of mental action: Modelling meta-awareness and attentional control with deep parametric active inference","volume":"7","author":"Hesp","year":"2021","journal-title":"Neurosci. Conscious."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.bandc.2016.02.008","article-title":"To be precise, the details don\u2019t matter: On predictive processing, precision, and level of detail of predictions","volume":"112","author":"Kwisthout","year":"2017","journal-title":"Brain Cogn."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1820","DOI":"10.1016\/j.visres.2011.06.012","article-title":"Magnocellular and parvocellular influences on reflexive attention","volume":"51","author":"Ries","year":"2011","journal-title":"Vis. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1146\/annurev.physiol.66.082602.092845","article-title":"Interpreting the BOLD signal","volume":"66","author":"Logothetis","year":"2004","journal-title":"Annu. Rev. Physiol."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Kuchling, F., Fields, C., and Levin, M. (2022). Metacognition as a consequence of competing evolutionary time scales. Entropy, 24.","DOI":"10.3390\/e24050601"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/8\/622\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:22:34Z","timestamp":1760109754000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/8\/622"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,24]]},"references-count":43,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["e26080622"],"URL":"https:\/\/doi.org\/10.3390\/e26080622","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,24]]}}}