Abstract: There may be structural principles pertaining to the general behaviour of systems that lead to similarities in a variety of different contexts. Classic examples include the descriptive power of fractals, the importance of surface area to volume constraints, the universality of entropy in systems, and mathematical rules of growth and form. Documenting such overarching principles may represent a rejoinder to the Neodarwinian synthesis that emphasizes adaptation and competition. Instead, these principles could indicate the importance of constraint and structure on form and evolution. Here, we document a potential example of a phenomenon suggesting congruent behaviour of very different systems. We focus on the notion that universally there has been a tendency for more volatile entities to disappear from systems such that the net volatility in these systems tends to decline. We specifically focus on origination and extinction rates in the marine animal fossil record, the performance of stocks in the stock market, and the characters of stars and stellar systems. We consider the evidence that each is experiencing declining volatility, and also consider the broader significance of this.