I am considering the same questions right now, thanks to the recent threads here.
I might be wrong, but one way to look at this specific example(colored balls/particles) is to consider that you determine the color of a particle when you, well, shine light on it. So when we say "color", what we really mean is "ways the body interacts with electromagnetic radiation". Specifically, how it absorbs and reflects it.
It is known that dark colors absorb more heat than light ones, and specifically blue absorbs more than red. So let's assume a (transparent) container containing red particles on the left and blue on the right. Otherwise, temperature is uniform. Now we let sunshine in the container, and the right sides heats up more than the left one. We can now use the difference in pressure in order to get work out of the system.
There is one things that kind of bugs me with the above though, which is that we have to put energy into the system in order to create a temperature difference between the sides. Seems there's an extra step compared to the the basic example, which is "fast vs slow moving particles". In that case the partition can just exploit the difference "passively" without us having to put energy into it.
I'm thinking that this is a consequence of the fact that, in order for one to physically measure an object's color, they must shine light on it, or at least that's what we have accepted in our setup. In this setup, "color" without the presence of EM radiation does not make physical sense. There has to be EM radiation interacting with the colored particles, because otherwise, what do we mean when we say "colored particles", in the confines of the particular setup?
Assuming we could construct a device that could differentiate between colors without shining light, but more "passively", say absorbing more energy from red particles than blue ones, then we could use that as a partition and again get work out of the system. That's the osmosis pressure example : if the partition can act as a membrane that lets red balls go through, that means it does absorb more kinetic energy from blue balls than red ones, so that does the job on its own. The membrane/partition would move.
In both cases, the initial setup is "left side differs from right side in property X, and this is how one can physically measure the difference in property X". Saying "red vs blue" is more ambiguous, but saying "left side interacts with light/membrane in X way while right side interacts with light/membrane in Y way" makes it much more clear what the property actually is, and how it can be exploited to do work.
I'm guessing that this means that the "colorblind" scenario is more of a rhetorical device that literal. If one wants to describe the model in its entirety, as if they were writing code for a computer, then it would be something like "left side absorbs such and such EM frequencies, when left side absorbs such and such frequencies". One being "colorblind" simply means they can't shine light on the container.
In any case, I still wonder if it can (or has) been proven in general that ability to differentiate between states means ability to exploit them to do work, but I guess it seems so. In the abstract, if we have a "black box" and we want to measure any property of it, we have to input some energy(even if it's in the form of a stationary body waiting to collide with another body) and then measure the differences in output. There must be differences in output, almost always in terms of energy/momentum, otherwise there wouldn't be any way to measure it in the first place.
(Please forgive me the long text and kind of disjointed thoughts but I am considering the same question right now, so if this should be removed as an answer, feel free to do so).
