In Complex Systems the collective behavior of the parts entails emergence of properties that can hardly, if at all, be inferred from properties of the parts. Science of Complex Systems provides radical new ways of understanding the physical, biological, ecological, and social universe. It helps reducing the gap between pure and applied science, establishing new foundations for the design, management and control of systems with levels of complexity exceeding the capacity of current approaches. Our approach is using efficiency as a measure of the extent to which input is well used for an intended task or function (output), and is often measured as the ratio of useful output to total input. Of course efficiency in complex systems refers to very different inputs and outputs in different fields.
Physical complex systems are open systems out of thermal equilibrium obeying the second law of thermodynamics and the principle of least action at the same time. To achieve maximum energy dispersal in order to increase entropy in the environment, they self-organize to provide flow network of channels for the energy flow through them. This flow network ensures the increasing efficiency in energy transmission through the system, as it evolves. Systems that are more efficient in energy dispersal, outcompete the less efficient ones for evolutionary survival. Biological and social systems are also complex systems, and there the efficiency of the system we define as the ratio of number of events: metabolic reactions, economic transactions, information transmitted through language, vs. the product of time and energy (action) that they consume. Therefore we define the level of organization of a system as the reciprocal of the average action efficiency for one event. This can be expressed as power, space, time and other form of efficiency in evolving complex systems. We are looking for a common framework to trace the increase of efficiency as a measure for level of organization and evolutionary stage of complex systems.
Moreover, approaching efficiency in complex systems in terms of simplicity, Murray Gell-Mann, physicist, raises the question: "In the description of nature, does deep simplicity always underlie apparent surface complexity?" Trying to use a definition for what might be simple or complex, Chaitin and Kolmogorov, mathematicians, described it as the minimum length of a message describing a system up to a given level of detail to a distant observer using a given grammar and vocabulary. However, there are usually different levels of description and at each level there are patterns that give the appropriate laws for that level. It is among those laws that one tends to find opportunities for practical reduction to more basic levels, with deep simplicity explaining away a great deal of the surface complexity.
Contributions from all disciplines that provide data for the increase of efficiency in the evolution of complex systems will move the field closer to the goal of creating a universal understanding of self-organization.
The original journal devoted to the science, mathematics and engineering of systems with simple components but complex overall behavior.
Efficiency as generally defined in different fields of complex systems mentioned in the next section.
Academia from different fields of complex system, including physics, mathematics, chemistry, biology, linguistics, computer science, sociology, and economics.
After the conference, full papers of the session are anticipated to be published in the proceedings of Springer Proceedings in Complexity.