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A Free Energy Principle for Biological Systems
Open accessAbstract
This paper describes a free energy principle that tries to explain the ability of biological systems to resist a natural tendency to disorder. It appeals to circular causality of the sort found in synergetic formulations of self-organization (e.g., the slaving principle) and models of coupled dynamical systems, using nonlinear Fokker Planck equations. Here, circular causality is induced by separating the states of a random dynamical system into external and internal states, where external states are subject to random fluctuations and internal states are not. This reduces the problem to finding some (deterministic) dynamics of the internal states that ensure the system visits a limited number of external states; in other words, the measure of its (random) attracting set, or the Shannon entropy of the external states is small. We motivate a solution using a principle of least action based on variational free energy (from statistical physics) and establish the conditions under which it is formally equivalent to the information bottleneck method. This approach has proved useful in understanding the functional architecture of the brain. The generality of variational free energy minimisation and corresponding information theoretic formulations may speak to interesting applications beyond the neurosciences; e.g., in molecular or evolutionary biology.
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“The Markov blanket can be further divided into 'sensory' and 'active' states that are distinguished in the following way: internal states cannot influence sensory states, while external states cannot influence active states [43].”
From Answering Schrödinger's question: A free-energy formulation (2018) · cites this paper as [43]
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Cites
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193
Information theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931
The free-energy principle: a unified brain theory?
Friston, K. (2010) · Nature Reviews Neuroscience · doi:10.1038/nrn2787 · Cited by 8,120 · cited 4×
“The following section is a brief summary of the material presented in [2].”
BackgroundInfluentialThe Origins of Order: Self-Organization and Selection in Evolution
Kauffman, S. A. (1993) · doi:10.1093/oso/9780195079517.001.0001 · Cited by 7,855
The origins of order; self organization and selection in evolution
Kauffman, S. A. (1994) · International Journal of Biochemistry · doi:10.1016/0020-711x(94)90119-8 · Cited by 6,753
Autopoiesis and Cognition: The Realization of the Living
Maturana, H. R., & Varela, F. J. (1980) · Boston Studies in the Philosophy and History of Science · doi:10.1007/978-94-009-8947-4 · Cited by 5,815
Rao, R. P. N., & Ballard, D. H. (1999) · Nature Neuroscience · doi:10.1038/4580 · Cited by 5,483 · cited 2×
“This is known as the Laplace assumption; see [14] for an introduction to predictive coding in visual neuroscience and [13] for an introduction to the Laplace assumption in the setting of variational free energy minimization.”
MethodA theory of cortical responses.
Friston, K. (2005) · Philosophical Transactions of the Royal Society B: Biological Sciences · doi:10.1098/rstb.2005.1622 · Cited by 4,578
The information bottleneck method
Tishby, N., Pereira, F. C., & Bialek, W. (2000) · arXiv · doi:10.48550/arxiv.physics/0004057 · Cited by 2,626 · cited 1×
“This is probably best illustrated when applying the free energy principle to the brain to understand its functional architecture [56] and the nature of neuronal codes [57].”
BackgroundThe Bayesian brain: The role of uncertainty in neural coding and computation
Knill, D. C., & Pouget, A. (2004) · Trends in Neurosciences · doi:10.1016/j.tins.2004.10.007 · Cited by 2,588
Research works printed but not linked: 1
- Nicolis, G., and Prigogine, I. (1977). Self-Organization in Non-Equilibrium Systems, John Wiley.
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Metadata
- Authors
- Karl, F.
- Affiliations
- The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, Queen Square, London, WC1N 3BG, UK
- ORCID
- Karl, Friston
- Venue
- Entropy
- Publisher
- MDPI AG
- Published
- 2012-10-31
- Volume
- 14
- Issue
- 11
- Pages
- 2100-2121
- ISSN
- 1099-4300 (ISSN-L)
- PMC
- PMC3510653
- OpenAlex
- W2154123408
- Cited by
- 377
- References
- 67
- Citations by year
- 2026: 19 · 2025: 40 · 2024: 29 · 2023: 31 · 2022: 59 · 2021: 47 · 2020: 32 · 2019: 35 · 2018: 17 · 2017: 11 · 2016: 17 · 2015: 15 · 2014: 14 · 2013: 11
- FWCI
- 6.56
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Entropy (publishedVersion, cc-by)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- UCL Discovery (University College London) (submittedVersion)
- Funders
- Wellcome Trust (088130)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Embodied and Extended Cognition
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- free energy principle, biological systems, circular causality, self-organization, slaving principle, nonlinear Fokker-Planck equation, random dynamical systems, attractor set, Shannon entropy, principle of least action, variational free energy, information bottleneck, brain functional architecture
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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