When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-Temporal scales might spontaneously arise. This non-Trivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems from physical to biological and social and is often related to collective behaviour. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems emergent properties, central theoretical questions to the study of emergence remain unanswered, such as the lack of a widely accepted,...