Complexity-Size and Complexity Rate-Size Rules in Stellar Evolution

An open question is how complex systems self-organize to produce emergent structures and properties. We explore the quantity-quality transition in natural systems. This is to say that the properties of a system depend on its size. More recently, this has been termed the complexity-size rule, which means that to increase their size, systems must increase their complexity, and that to increase their complexity they must grow in size. We apply the complexity-size rule to stars to compare them with other complex systems in order to find universal patterns of self-organization independent of the substrate. As a measure of complexity of a star, we are using the degree of grouping of nucleons into atoms, which reduces nucleon entropy, increases the variety of elements, and changes the structure of the star. As a measure of the rate of self-organization and increase in complexity, we are using the average rate of nucleosynthesis over the lifetime of stars as a function of their mass. Here we find that, as for the other systems studied, the complexity of stars and the rates of increase of complexity are in a power law proportionality with their size. The bigger a system is, the higher its level of complexity is and the faster the rate of its increase - despite differing explosion energies and initial metallicities from simulations and data, which confirms the Complexity-Size and Complexity Rate-Size rules and our model. The complexity and the rate of increase of complexity of a star are also in a power-law relation with each other.