Phase transitions in complex systems An information geometric approach

We live in a complex world. Whether we look at chemical reactions in a reactor, networks of neurons in the brain, or human societies, a fascinating multi-level, non-linear system appears. The field of complexity has set it as a goal to study the common denominator of these systems, which are usually studied separately in disparate academic disciplines.
Since the premise of complexity research is that there exists a common denominator, a question arises about what will be the conceptual and mathematical framework that can unite these phenomena. In my thesis I explore the possibility that critical phenomena in complex systems can be studied using a framework called Information Geometry. The idea is borrowed from geometrical statistical mechanics where the information geometry of many models exhibiting phase transitions have been studied and some researchers have even gone so far as to suggest the geometrical properties as a definition for critical transitions.
The intuition is simple – when a system is described in statistical terms, its different phases will invariably have different statistical properties. The sudden change in these properties can be used to define the phase transition line. Inverting the question one can term this as an inference problem – given the statistical properties of the system, how well can we measure the underlying control parameters that govern the transition. At the phase transition point, where the change in statistical properties is large, the value of the parameter is easy to infer. Therefore one can use the Fisher information to detect the phase transition.