Civilization and prosperity may be a function of energy per capita -- aka "White's law."
That doesn't work. Except for the weasel word "may be". Yes, it "may be", but it's not.
civilization and prosperity is much more closely tied to how energy is aggregated and distributed. likewise for wealth.
to show this, one can imagine two extreme scenarios:
1.) all energy goes to a single person, everyone else gets no energy. in this scenario the energy per capita could be extremely high, or extremely low. it doesn't much matter, because the total productivity from that energy will be capped by the person's ability to make use of it. and that ability is capped by the limits of a single person's brain power, as well as by how fast they can move their fingers, feet, etc. this is obviously a very low prosperity situation. it can be argued that that was already given from the outset, since almost everyone has no energy.
2.) randomly distributed energy. the production efficiency is not as bad as scenario 1, since the wasted energy is not the total energy minus the capacity of one person, but there is still a lot of energy wasted, and still a lot of things that could use more energy. and while energy a priori is necessarily distributed more fairly than the first scenario (since the first scenario is the most unfair distribution.), it still leaves a lot of people out of "prosperity" and a lot of people who's prosperity isn't really effected any more by energy level because they already have more than their capacity.
so you see even in very high energy or very low energy per capita, you could get drastically different prosperity levels. having said that, while yes, prosperity is "a function of..." it is so in the sense that energy per capita is one variable in a much larger equation with many other variables, and the final result of the equation is rather weakly correlated with energy per capita. and it is in fact, not correlated at all with wealth per capita, since that is simply a matter of the amount of currency in circulation; a more predictive economic indicator is the ability of individuals to exchange goods and services for absolute benefit.
in either case it is not so much a matter of total quantities in the aggregate, but relative proportions in the parts.