My point is that this exact ability will be, one day, done better by a machine. The day that machines become more creative than humans is the day I'm talking about.
Why would machines have more entropy? Replication and acquiring knowledge faster is not an increase in entropy.
A human brain is nothing else but a piece of physics, a data processor. There's no reason that a silicon version of it cannot be better at everything that a human brain can do, including creativity.
You didn't even comprehend my point about entropy then. Try again to read the Information is Alive! essay and think more carefully about it.
It is our interaction biologically with our environment over long periods of evolution that has given us the extremely high entropy that we can't transfer to machines (because it would require the machines be each one of us because none of us can totally comprehend the entire network of all of us). That entropy is buried not only in our genes but in our living biology (which includes the billions of variants of living personalities, cultures, etc). The robots could process information faster, but that gives them no inherent evolutionary advantage in terms of resilient creativity and adaptation due to the historical accumulation of entropy in the species.
This is why it is much more likely that the advantages of machines become incorporated into our species.
Machines can easily have bigger entropy sources than biological entities. Biological entities derive their evolutionary source of entropy from random mutations. I don't know what the entropy flux is, but it is monstrously low. Maybe a few bits per year for a whole species. The other entropy source is the random recombination of DNA during sexual reproduction. If it is a megabyte per procreation, it is a lot.
The genes are not the largest store of entropy in our species. The encoding our entropy is in the living network of the species. Our network is alive also, analogous to the brain of ants is the collective brain of the colony. Our entropy is on the magnitude of some exponential or perhaps factorial of a billion (will need to think this out a bit when I have more time).
True random number generators, based upon physical noise, can provide machines with entropy sources of tens of megabytes per second using a few transistors only. Machines outsmart us already concerning entropy sources.
When we speak about entropy in this context we differentiate noise from Shannon information. So your noise generator is not applicable.
And all processing that a brain can do is deterministic, or stochastic (which is nothing else but deterministic with a true random generator as input, Monte Carlo style). So there's nothing that a human brain can think off, that a machine cannot think off.
You are thinking about the system of the species by looking at one brain in isolation. That is very myopic. The value is in the diversity of the network.