Again, this is very different from the situation with entropy. I think you’re confusing two meanings of the word ‘model’. It’s one thing to have an incomplete description of the physics of the system (for instance, lacking nuclear forces, as you describe). It’s another to lack knowledge about the internal microstates of the system, even if all relevant physics are known. (In the statistics view, these two meanings are analogous to the ‘model’ and the ‘parameters’, respectively). Entropy measures the uncertainty in the distribution of the parameters. It measures something about our information about the system. The most vivid demonstration of this is that entropy changes the more you know about the parameters (microstates) of the system. In the limit of perfect microstate knowledge, the system has zero entropy and is at absolute zero. But energy (relative to ground state) doesn’t change no matter how much information you gain about a system’s internal microstates.
Again, this is very different from the situation with entropy. I think you’re confusing two meanings of the word ‘model’. It’s one thing to have an incomplete description of the physics of the system (for instance, lacking nuclear forces, as you describe). It’s another to lack knowledge about the internal microstates of the system, even if all relevant physics are known. (In the statistics view, these two meanings are analogous to the ‘model’ and the ‘parameters’, respectively). Entropy measures the uncertainty in the distribution of the parameters. It measures something about our information about the system. The most vivid demonstration of this is that entropy changes the more you know about the parameters (microstates) of the system. In the limit of perfect microstate knowledge, the system has zero entropy and is at absolute zero. But energy (relative to ground state) doesn’t change no matter how much information you gain about a system’s internal microstates.
I understand what you are saying, but I am not convinced that there is a big difference.
How would you change this uncertainty without disturbing the system?
How would you gain this information without disturbing the system (and hence changing its energy)?
EDIT: see also my reply to spxtr.
You have to define what ‘disturbing the system’ means. This is just the classical Maxwell’s demon question, and you can most definitely change this uncertainty without changing the thermodynamics of the system. Look at http://en.wikipedia.org/wiki/Maxwell%27s_demon#Criticism_and_development
Especially, the paragraph about Landauer’s work is relevant (and the cited Scientific American article is also interesting).