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Phase Transitions (Primers in Complex Systems)

Sole, Ricard V.
Princeton University Press: Princeton, NJ, 2011
ISBN 9780691150758 (pb)

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Reviewed by Emile Chappin
Energy and Industry Section, Faculty of Technology, Policy and Management, Delft University of Technology

Cover of book This book is on the state of the art on 'phase transitions': complex systems with qualitatively different patterns of organization, separated by sharp boundaries. The phase shift from a spreading epidemic to one in decline, is conceptualized as a discontinuous jump in the system's state between both organizational patterns. From a mathematical perspective, Solé clearly defines such phases, transitions between them, and elegantly shows how transitions in complex systems from various domains - not only epidemic spreading and cancer, but also ecological shifts and collective intelligence - can be brought down to a useful representation. He explains concepts clearly, both in text and by means of strong visualizations. The book can be divided in a theoretical part and a set of applications. Although the chapters are relatively short, the book is well embedded in the literature on the topic of phase transitions as well as on each of the cases. Solé warmly invites the reader along; he provides ample references for further reading as well.

The first five chapters read like a textbook introduction on the topic and focus on theoretical concepts. The book by necessity is not limited to phase transitions as such, but also introduces the behavior of dynamic systems and some properties of complex systems in general. And Solé uses many simple examples to show what concepts such as stability, bifurcation, percolation and path dependency mean and how they can be defined.

The other eleven chapters in the book are devoted to practical applications of mathematical models of dynamic (social) systems that focus on various aspects of phase transitions. The range of applications is surprising. Solé covers small systems such as cancer cells or genes, as well as large systems such as congestion in road traffic and the fall of ancient societies. He follows a minimalistic perspective and typically focuses on representing the studied systems in continuous mathematical equations and two-dimensional grids. He shows for each system, both analytically and graphically, what behavior can be expected under variation of the chosen set of two to three parameters. In each case, this approach leads to four findings: 1) what phases can be expected, 2) what phases exist under what combinations of parameters and 3) when phase transitions may occur, and 4) whether these phase transitions are irreversible. Each of these chapters shortly ends with some implications.

If one would have to be critical regarding this book, three issues could be noted. First, the focus on end-states is strong. Change in the dynamic systems are essentially interpreted as a classification of possible end-states for a system: the phases. The transition between those phases could have received more attention. Secondly, the book mainly analyses systems by identifying the core properties related to phases and phase transitions. More opportunities for the design of such systems, the improvement of existing systems and the steering of changes could have been identified. Finally, a synthesis part in the book would have been welcome, regarding 1) what the research on phase transitions has brought us so far, 2) how the methodology limits the interpretation, the analysis, and the recommendations that are or could be identified from this volume, and 3) where the research may or should go from here.

Solé has compiled an interesting overview of the vast amount of real world systems in which phases play a role. It is a good introduction to the topic and the great variety of applications is inspirational. Phase Transitions is a good read for the JASSS audience interested in if, how, and when abrupt changes may occur - either as risks for collapse or as opportunities for salvation.


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