Ok, if you really want to get into this: physics is a relationship between an observer and "the rest of the universe".  That "rest of the universe" contains entities which the first observer might identify as observers (I will call them "secondary observers"), and in order for his physics to be consistent, whatever the first observer observes from those secondary observers, must be coherent with what the first observer observes, and what he would observe if he were in the place of those secondary observers.   In other words, the only consistency must come from what the first observer observes "directly" and what he observes when observing those secondary observers.   This is the "consistent history" view of physics.  At no point, an observer "needs to prove" anything to a secondary observer.  He simply needs a consistent view between his "direct observations of nature" and his "observations of other observer entities".

The idea that there is a single objective reality out there goes out of the window with that view, but for an observer, the consistent view of his observations of nature, and his observation of secondary observers, is what comes closest to his best guess of what his objective reality might look like.

This kind of consistent history approach (first formulated if I remember correctly by Gell Mann in the 1960ies) explains very easily a lot of quantum "paradoxes", like the EPR "paradox", and also explains apparent paradoxes like Maxwell's demon.

In as much as those "secondary observers" are actual observers of their own, what is needed for everything to be consistent is that they too, in THEIR view of reality, see the first observer as consistent with that.

The simplest solution to this is that all observers observe the same objective reality, which is a classical viewpoint, but difficult to reconcile with quantum mechanics.  But it is not the only solution to this, and "consistent histories" is another, much more complicated, but quantum mechanically compatible, view of things.  If you want to stick to the classical "objective world" view, you have to introduce many strange things in order to explain quantum mechanical effects, such as "spooky action at a distance", "non-causal effects going back in time" and other weird things, while consistent histories don't need all that stuff.

In the same vein, entropy is a relationship between an observer and a system: it is his ignorance about the system's micro state.  In as much as another observer DOES know this micro state (like Maxswell's demon), then that system has no entropy wrt to that secondary observer, but that secondary observer now has entropy wrt to the primary one.

However, in most all cases, "human observers" don't know microstates and hence, they all agree more or less on the physical entropy of most objects, give or take a few bytes.

A secret key has no entropy with respect to its owner, and has (hopefully) full entropy wrt to an attacker.  Maxwell's demon is like the guy with his secret key: he known the micro state of the gas ; but as such, the demon has as much entropy wrt us, than the gas itself.