PHYSICAL COMPLEXITY AND ZIPFS LAW

This article deals with a measure of the complexity of a physical system recently proposed by Schapiro and puts it into the context of other recently discussed measures of complexity. We discuss this new measure in terms of a simple Mar-kovian evolution model, extending and specifying the model given by Schapiro, which has the advantage of being analyically tractable. We find that the proposed complexity measure leads to interesting results: there exists a kind of phase transition in this system with a vanishing value of the probability c of generating a new species. This phase transition is related to a specific complexity of about 3 bits. By investigating decreasing c (c approximately N(-q), N the total number of individuals), we find that the complexity per species grows monotonically with q, diverging logrithmically with N as q goes to infinity.