Title
Phase transition in random catalytic networks Phase transition in random catalytic networks
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Melville, N.Y. :American Physical Society ,
Subject
Physics
Source (journal)
Physical review : E : statistical, nonlinear, and soft matter physics / American Physical Society. - Melville, N.Y., 2001 - 2015
Volume/pages
72(2005) :3 Part 2 , p. 1-7
ISSN
1539-3755
1550-2376
1539-3755
Article Reference
036117
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/7da100/6196.pdf
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