According to the no-hiding theorem (see https://en.wikipedia.org/wiki/No-hiding_theorem), information is truly and generally conserved within any isolated system. According to Noether's theorem (https://en.wikipedia.org/wiki/Noether%27s_theorem), to every symmetry of an action there corresponds a conservation law. If I understand Noether's theorem correctly, the conserved quantity is the generator of changes in the quantity that is behind the symmetry of the action. Furthermore, according to Ron Maimon's answer in Is the converse of Noether's first theorem true: Every conservation law has a symmetry?, there must be a symmetry to every generally conserved quantity.
Now, separately, I found that according to https://en.wikipedia.org/wiki/Physical_informationa one physicist (B. Frieden) had made an (as yet un-proven) claim (called extreme physical information on Wikipedia) along the lines of that minimizing a change in information would effectively lead to the same result as minimizing the action.
As such, I would like to know: If we take the change in a system's information, $\Delta I$, to be proportional to that system's Euclidean action, $-S_E/\hbar$, then: 1st, what is the symmetry behind information conservation; and 2nd, (and most importantly) what is information generating changes in?
