EXCERPT To date, there is no universally accepted definition of complexity. All definitions, however, agree on the fact that there are two fundamental characteristics of a complex system: a multiplicity of constituent elements, and the presence of non-negligible interactions between them. This definition, although very general, is sufficient to exclude from the picture most of the systems that have traditionally been studied by physics. Newtonian physics, in fact, although able to study systems of bodies interacting with one another, through gravitational or electrostatic force for example, can provide exact predictions only when that interaction is limited to a maximum of two objects. This limit is known as the three body problem, according to which, in general terms, it is not possible to derive an analytical equation of the Newtonian trajectory of three bodies in reciprocal interaction. Statistical thermodynamics, as formalised by physicist Ludwig Boltzmann in the 1870s, made it possible to understand the laws governing heat transfer in macroscopic bodies as the result of the microscopic movements of atoms. By its very nature, therefore, Boltzmann’s thermodynamics is concerned with studying systems made up of an enormous number of components. But rather than being followed individually in their own trajectories, here they are treated collectively from a statistical point of view. Boltzmann’s thermodynamics paved the way for the study of the processes of the organisation of matter; however, its principles appear to contradict the possibility that a system could spontaneously maintain an organised structure.…