Assuming the phenomenon is real (and I'm not going to take the trouble to find out there are all sorts of trivial one, and some non-trivial ones that really don't add much explanatory power.
For example of the latter, how about the observation that social inequality past a certain point tends to perpetuate itself and increase? A and B have more than C-Z, in some sort of system that competes for power, capitalist, feudal, bronze age empire, whatever--any sort of class society with significant production above subsistence. A-Z compete with one another but also cooperate in a social system which has lots of rigid rules for cooperation. A+B have more influence than c-z, but maybe not than everybody combines. So they use their power to campaign for a rule change that will given them a bit more. They avoid united opposition from c-z in various ways. Maybe they make sure the changes hurx only x-z. Maybe they have ability to make friends of someone who is an especially skilled deceiver to prevent serious opposition. At any rate, the power differential between them and everybody else increase. A year later they push through another rule change. The cycle continues, and of course similar processes go on among c-z. And of course it is overly simple, even including multiple classes igores inequality among mulitiple dimensions, gender, race/nationality/cultural sub-group. And this is unbelievable trivial; but you could probably add a few constraints and end up with a Gibbs distribution, given a minimum initial surplus, and minimal starting inequality.
Maybe this can produce something useful, but I doubt you will end up with much more than a statistical restatement of "Accumulate, accumulate! That is Moses and the prophets! ", without either descriptive or predictive value.