Solitary, poor, nasty, brutish, and short -- those are all low energy high entropy states.
The opposite of solitary is cooperating and connecting and that's provably difficult to achieve (see game theory). Brutish is also a game theoretic "all defect" scenario which is very likely. Cooperation and peace are harder to achieve and require more sophisticated game playing strategies that integrate results over multiple iterations.
Poor, nasty, and short describes low energy high disorder states.
So ultimately the question is how and why do we exceed the bare minimum, because exceeding the bare minimum state required for survival and procreation is pretty much the definition of a great or exceptional society or period of history.
Solitary is high entropy for early humans. People cannot survive alone (lets say even with mating partner but no tribe equals alone). At least not without training. Tribe ejection is a severe punishment.
Disjoint tribes might be the low entropy?
But still, it is interesting to consider that the three phenomena he talks about -- poverty, crime, and ignorance -- are now mostly thought of as aberrations from the norm that needed to be eliminated, when in fact they're the state that the vast, overwhelming majority of humans in history were born, lived and died in.
If you do think of the problems in the reverse way -- how do we _increase wealth_, and _increase cooperation_ and _increase knowledge, they're all become sort of the _same problem_ -- ie: how do we as a society increase the benefits of cooperation with each other? You see the problem of tackling crime not as a problem of devising the correct punishment scheme, but as devising a way such that the benefits of cooperation outweigh the benefits of free riding.