Imagine a maximum entropy information system: This system would hold meaningful information, not just random noise, but still be of maximum possible entropy in the sense that you could randomly change the order of the smallest bits of information in it without actually changing the overall information it contains. You can toss and dice the information bits as much as you want, the overall information stays the same. Kinda like taking all the words of War and Peace, putting them into a bucket, stirring properly, emptying the bucket on the blank pages and ending up with exactly the same exciting story. It is irrelevant what the system is made of, if it's physical or logical doesn't matter for this thought experiment. It is also irrelevant whether such a system is possible or not, lets just assume it does exist. Now, the thing I can't wrap my head around: What would be the implications of such a system? What other properties would the known properties imply? What would be the theoretical requirements for such a system to be possible in the first place? What would the properties of the system tell us about the properties of the information bits it contains? I would suspect there must be symmetries? Any thoughts on this very appreciated!