what is the notion of information in physics
Information in physics seems to assume a metamodel of what attributes characterize a system state. The uncertainty you mention is in terms of this metamodel of what is important in characterizing a system. Is this true?
So, if I understand you correctly, information in the physics sense is creating a map of the territory of reality. And then the notion of conservation of information relates to conserving that map, i.e., using that map to recreate the territory it is depicting. Is that correct?
Is there a problem in this metamodel that assumes that there are a finite number of states that a system can be in? What if the number of states is infinite? Would that negate the validity of the map?