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NAKFI 2008 - Complex Systems

Emergence and collective phenomena in equilibrium and nonequilibrium systems
Nigel Goldenfeld 

In this tutorial, Goldenfeld describes the connections between complex phenomena and emergent phenomena in simple systems.  He begins with a discussion of emergence in a very simple context: the way in which a fluid can become a solid at low temperatures, and shows how interactions between atoms give rise to collective modes of the system, such as sound waves.  Next he discusses the way in which emergent phenomena need to be understood in terms of the level of description; and this leads into the interesting issue of what we mean by "fundamental" laws in science.  He then turns to the signatures of emergence, including emphasis on the connections with fluctuations and scaling phenomena.  Finally, two recent examples taken from Goldenfeld's own interests are described: (1) turbulence as an emergent phenomena, and (2) the important role of collective phenomena in early evolution.