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Phase transition in random catalytic networks
Open accessAbstract
The notion of (auto)catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this long-standing problem is possible by mapping the problem onto a set of nonlinear recurrence equations. The solution of these equations shows a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to fully understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other. We observe a remarkable similarity of the solution of the system and the PVT diagrams in standard thermodynamics.
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Other transitions involve the jump to novel properties associated with increased network connectivity, such as the emergence of autocatalytic cycles out of random chemical reactions once the number of possible reactions crosses the percolation threshold.
“Other transitions involve the jump to novel properties associated with increased network connectivity. This would be the case of the emergence of autocatalytic cycles out of random chemical reactions (figure 10c) once the number of possible reactions crosses the percolation threshold (a non-equilibrium phase transition) [381–384].”
From Fundamental constraints to the logic of living systems (2024) · cites this paper as [383]
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Research works printed but not linked: 9
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The evolutionary ecology of technological innovations
Solée, R. V., Valverde, S., Casals, M. R., Kauffman, S. A., Farmer, D., & Eldredge, N. (2013) · Complexity · doi:10.1002/cplx.21436 · Cited by 140
Self-citationFundamental constraints to the logic of living systems
Solé, R., Kempes, C. P., Corominas-Murtra, B., De Domenico, M., Kolchinsky, A., Lachmann, M., Libby, E., Saavedra, S., Smith, E., & Wolpert, D. (2024) · Interface Focus · doi:10.1098/rsfs.2024.0010 · Cited by 34
Metadata
- Authors
- Hanel, R., Kauffman, S. A., & Thurner, S.
- Affiliations
- University of Antwerp (BE)
- Santa Fe Institute (US)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2005-09-16
- Volume
- 72
- Issue
- 3
- Pages
- 036117-036117
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W1621366770
- Cited by
- 42
- References
- 0
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 5 · 2023: 1 · 2022: 1 · 2020: 1 · 2019: 1 · 2017: 2 · 2016: 1 · 2015: 1 · 2014: 3 · 2013: 3 · 2012: 3
- FWCI
- 1.55
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science Foundation Ireland
- Austrian Science Fund (P17621)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Origins and Evolution of Life
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- autocatalytic networks, phase transitions, product variety, order parameter, origin of life, chemical reaction networks
- MeSH terms
- Algorithms, Catalysis, Cell Physiological Phenomena, Computer Simulation, Enzymes, Models, Biological, Models, Chemical, Proteins, Models, Statistical, Signal Transduction, Phase Transition
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