be collected, stored, analyzed, and visualized, and they have made possible numerical simulations using very sophisticated models.
In this chapter, the committee describes five areas of complex system research: the nonequilibrium behavior of matter; turbulence in fluids, plasmas, and gases; high-energy-density systems; physics in biology; and Earth and its surroundings.
The most successful theory of complex systems is equilibrium statistical mechanics—the description of the state that many systems reach after waiting a long enough time. About a hundred years ago, the great American theoretical physicist Josiah Willard Gibbs formulated the first general statement on statistical mechanics. Embodied in his approach was the idea that sufficiently chaotic motions at the microscopic scale make the large-scale behavior of the system at, or even near, equilibrium particularly simple. Full-scale nonequilibrium physics, by contrast, is the study of general complex systems—systems that are drastically changed as they are squeezed, heated, or otherwise moved from their state of repose. In some of these nonequilibrium systems even the notion of temperature is not useful. Although no similarly general theory of nonequilibrium systems exists, recent research has shown that classes of such systems exhibit patterns of common (“universal”) behavior, much as do equilibrium systems. These new theories are again finding simplicity in complexity.
Everyday matter is made of vast numbers of atoms, and its complexity is compounded for materials that are not in thermal equilibrium. The properties of a material depend, then, on its history as well as current conditions. Although materials in thermal equilibrium can display formidable complexity, nonequilibrium systems can behave in ways fundamentally different from equilibrium ones. Nature is filled with nonequilibrium systems: Looking out a window reveals much that is not in thermal equilibrium, including all living things. The glass itself has key properties, such as transparency and strength, that are very different from those of the same material (SiO2) in the crystalline state. Essentially all processes for manufacturing industrial materials involve nonequilibrium phenomena.
A few of the many examples of matter away from equilibrium are described below.