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Relating Fisher information to order parameters.
Abstract
We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix. The assumptions that we make limit our analysis to order parameters representable as a negative derivative of thermodynamic potential over some thermodynamic variable. Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of the Fisher information matrix to the rate of change in the corresponding order parameters. The obtained relationships allow us to identify, in particular, second-order phase transitions via divergences of individual elements of the Fisher information matrix. A computational study of random Boolean networks supports the derived relationships, illustrating that Fisher information of the magnetization bias (that is, activity level) is peaked in finite-size networks at the critical points, and the maxima increase with the network size. The framework presented here reveals the basic thermodynamic reasons behind similar empirical observations reported previously. The study highlights the generality of Fisher information as a measure that can be applied to a broad range of systems, particularly those where the determination of order parameters is cumbersome.
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“Fisher information, which has been shown to be related to phase transitions (Prokopenko et al., 2011).”
From Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis (2013) · cites this paper as Prokopenko et al., 2011
In the citing paper
“C is correlated with Fisher information, which has been shown to be related to phase transitions (Prokopenko et al., 2011).”
From Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis (2013) · cites this paper as Prokopenko et al., 2011
Citations
Cites
Information theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931
The Origins of Order: Self-Organization and Selection in Evolution
Kauffman, S. A. (1993) · doi:10.1093/oso/9780195079517.001.0001 · Cited by 7,855
Self-organized criticality: An explanation of the 1/ f noise
Bak, P., Tang, C., & Wiesenfeld, K. A. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.381 · Cited by 7,644
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
Ziegel, E. R., Lehmann, E. L., & Casella, G. (1999) · Technometrics · doi:10.2307/1270597 · Cited by 4,203
Information Theory and Statistical Mechanics. II
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.108.171 · Cited by 3,253
Computation at the edge of chaos: Phase transitions and emergent computation
Langton, C. G. (1990) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(90)90064-v · Cited by 1,527
Haken, H. (1983) · Springer series in synergetics · doi:10.1007/978-3-642-88338-5 · Cited by 1,471
Theory of first-order phase transitions
Binder, K. (1987) · Reports on Progress in Physics · doi:10.1088/0034-4885/50/7/001 · Cited by 1,095
Random Networks of Automata: A Simple Annealed Approximation
Derrida, B., & Pomeau, Y. (1986) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/1/2/001 · Cited by 688
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Research works printed but not linked: 6
- X. R. Wang, 2010, Proceedings of the 12th International Conference on the Synthesis and Simulation of Living Systems (Alife XII), Odense, Denmark
- C. Gershenson, 2004, Proceedings of the Workshops and Tutorials of the Ninth International Conference on the Simulation and Synthesis of Living Systems (ALife IX), Boston
- B. Derrida, 1990, Fundamental Problems in Statistical Mechanics VII Altenberg, Germany, 1989
- C. Gershenson, 2004, Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems (ALife IX), Boston
- J. T. Lizier, 2007, Proceedings of the Ninth European Conference on Artificial Life (ECAL 2007), Lisbon, Portugal
- 10.1002/(SICI)1099-0526(199901/02)4:3< 47::AID-CPLX9> 3.0.CO;2-V · DOI
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Metadata
- Authors
- Prokopenko, M., Lizier, J. T., Obst, O., & Wang, X. R.
- Affiliations
- Commonwealth Scientific and Industrial Research Organisation (AU)
- Max Planck Institute for Mathematics in the Sciences (DE)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2011-10-13
- Volume
- 84
- Issue
- 4
- Pages
- 041116-041116
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W1971124708
- Cited by
- 122
- References
- 34
- Citations by year
- 2026: 10 · 2025: 4 · 2024: 4 · 2023: 3 · 2022: 8 · 2021: 9 · 2020: 8 · 2019: 6 · 2018: 15 · 2017: 16 · 2016: 7 · 2015: 3 · 2014: 14 · 2013: 12 · 2012: 3
- FWCI
- 6.92
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- Fisher information matrix, order parameter, phase transitions, second-order phase transition, critical points, random Boolean networks, thermodynamic potential, finite-size scaling, critical phenomena
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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