On the independence of correlated events

Why do some quite complex events appear to be built up from seemingly independent elementary events? It is, of course, fortunate that this is so, for otherwise, it would be hard to analyze the world around us. But the technical question remains. It is here argued that a sufficient condition is that the possible complex events all have the same sum(s) for (one or more) additive variable(s). Constants of the motion are one example of such variables. In addition, it is shown that the independent distribution of the elementary events is one of maximal entropy.