Energy and the origin of life

The Financial Times reviews Nick Lane, The Vital Question:

The key moment for the evolution of life on Earth, Lane says, came at some point between 2bn and 1.5bn years ago. Then, in a rare and remarkable act of “endosymbiosis”, an archaean absorbed a bacterium — and this combination survived to divide into a rapidly evolving chain of descendants. All eukaryotic creatures, including ourselves, come from this once-in-4bn-years union.

Lane puts energy at the centre of his story, deploying thermodynamic and chemical arguments that will be challenging but not incomprehensible for the general reader. Although all living creatures generate energy by pumping protons across a membrane, the combined cell could deploy energy resources far beyond the scope of bacteria or archaea on their own. The absorbed bacteria multiplied within their archaean host cells, losing their independent identity and evolving into the minute power packs that we know as mitochondria. In the process they lost most of their DNA but retained a tiny genome critical for energy processing. 

This internal specialisation enabled eukaryotic cells to generate many thousands of times more energy per gene than prokaryotes.

I'm wondering about the informatics of this. Years ago Dave Hays and I argued that evolution produces complexity by using a relatively small amount of energy to buy information that in turn allows the purchase of more energy than the cost of the information increment plus the energetic cost of the purchase. Is that what's going on here?

H/t 3QD.