How would you change this uncertainty without disturbing the system?
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).
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).