However, it faces some competition. In particular maximum entropy thermodynamics also purports to explain essentially the same range of phenomena.
This leads to the question of what the relationship between these ideas is - and whether we really need both of them.
Since maximum entropy thermodynamics and the maximum entropy principle are still little known about and poorly understood, I should probably start by explaining what these ideas are all about. However, a proper summary would probably take a while. So very briefly, here, we'll be using maximum entropy to refer to the idea that maximizing entropy explains many of the irreversible dynamics seen in the universe. In other words, the world behaves so as to maximize entropy.
Maximum entropy is quite different from the second law of thermodynamics. The second law of thermodynamics says that entropy rarely decreases. Maximum entropy says that entropy is maximized. Those are very different ideas. Maximum entropy constrains expectations a lot more than the second law does.
It is clear that Universal Darwinism and maximum entropy thermodynamics are very similar. Maximum entropy thermodynamics represents a good thermodynamic characterization of universal Darwinism. The two ideas evidently have a massive overlap in their domains of application and the predictions they make.
Their similarity is surprising if you look at the contents of the two theories. They seem to have quite different structures. However, it was observed by Lotka back in 1922 that the maximum entropy applies to living systems. Since then we have developed an understanding of why that is so: organisms compete to reach sources of order first. Organisms need order to fuel their living processes. They also try and keep such sources of order away from competitors, sometimes even if that involves destroying those resources.
Universal Darwinism scores some points over maximum entropy thermodynamics in cases of sophisticated systems. The somewhat distinct goals of complex living systems can be usefully understood as products of low level entropy maximization via the idea of goal delegation.
Both ideas apply to irreversible systems. Reversible dynamics lead to no change in entropy. Similarly, in universal Darwinism, mutation and selection means that something has to die or be lost. I am not talking about microscopic reversibility here, but macroscopic reversibility - i.e. Humpty Dumpty.
I think that the literature in each of these two fields should substantially enrich the other. Rather than competing, I hope that they will complement each other.
However, both ideas are currently surrounded by much confusion and controversy. Neither is popular or well established. I hope that their union will prove to be a constructive one.