Equilibrium Systems

As mentioned in the introductory chapter, the complex systems one is interested in "complexity studies" are usually those that consist of a large collection of interacting sub-units and that are out-of-equilibrium. Such systems, or rather simplified models of the realistic systems, have become accessible to study in the last two decades due to the explosive growth in computer power at decreasing costs. We will study such out-of-equilibrium complex systems in subsequent chapters, but here we will focus our attention on simpler equilibrium systems. However even a large system in equilibrium is not easy to describe and understand analytically. Nonetheless, beginning already In the nineteenth century brilliant minds applied themselves to the problem and developed the fields of thermodynamics, kinetic theory and statistical mechanics. Some of the concepts that have been developed for the description of phenomena in equilibrium systems turn out to be relevant also for the study of more realistic out-of-equilibrium complex systems that occur in nature. Indeed, the study of equilibrium systems gives a concrete and quantitative illustration of the concepts of entropy, emergent laws and universality.