The DOI matches its Crossref record; 32 of the 34 references it cites were found in a registry or an index.
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
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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
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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
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- C. Gershenson, 2004, Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems (ALife IX), Boston
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- 10.1002/(SICI)1099-0526(199901/02)4:3< 47::AID-CPLX9> 3.0.CO;2-V · DOI
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JIDT: An Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems
Lizier, J. T. (2014) · Frontiers in Robotics and AI · doi:10.3389/frobt.2014.00011 · Cited by 391
Self-citationDeffner, S., & Campbell, S. (2019) · Morgan & Claypool Publishers eBooks · doi:10.1088/2053-2571/ab21c6 · Cited by 376
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Hauke, P., Heyl, M., Tagliacozzo, L., & Zoller, P. (2016) · Nature Physics · doi:10.1038/nphys3700 · Cited by 362
Parameter Space Compression Underlies Emergent Theories and Predictive Models
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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
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