> But entropy is also something that we can get from experimental measurements. In this case, the experimental setup does not care about microstates and macrostates, it just has properties like enthalpy, heat capacity and temperature. […] experimental measurements of the entropy of a given materials are consistent and independent of whatever model the people doing the experiment were operating on. Fundamentally, entropy depends on the probability distribution, not the observer.
Thermodynamics does have the concept of the entropy of a thermodynamic system; but a given physical system corresponds to many different thermodynamic systems. […] It is clearly meaningless to ask, “What is the entropy of the crystal?” unless we first specify the set of parameters which define its thermodynamic state. […] There is no end to this search for the ultimate "true" entropy until we have reached the point where we control the location of each atom independently. But just at that point the notion of entropy collapses, and we are no longer talking thermodynamics! […] From this we see that entropy is an anthropomorphic concept, not only in the well-known statistical sense that it measures the extent of human ignorance as to the microstate. Even at the purely phenomenological level, entropy is an anthropomorphic concept. For it is a property, not of the physical system, but of the particular experiments you or I choose to perform on it.
It is though. Temperature is an aggregate summary statistic used when the observer doesn't know the details of individual particles. If you did know their position, speed and velocities, you could violate the laws of entropy as Maxwell's thought experiment demonstrated in 1867 https://en.wikipedia.org/wiki/Maxwell%27s_demon
Maxwell's demon is a thought experiment that involves a magical being. It's an interesting thought experiment, and it provides some insights about the relationship between macro states and micro states, but it's not actually a refutation of anything, and it doesn't describe any physically realizable system, even in theory. There is no way to build a physical system that can act as the demon, and so it follows that entropy is not actually dependent on the information actually available to physical systems.
This is obviously visible in the observer-independence of many phenomena linked to temperature. A piece of ice will melt in a large enough bath of hot water regardless of whether you know the microstates of every atom in the bath and the ice crystal.
"large enough" and "bath" is doing a lot of work here. I don't think it's necessarily about size. It's about that size and configuration implying the particle states are difficult to know.
If for example, you had a large size but the states were knowable because they were all correlated, they were following a functionally predictable path, for example all moving away from the ice cube, or all orderly orbiting around the ice cube in a centrifuge such that they didn't quite touch the ice cube, it wouldn't melt.
The ice cube would melt, it would just take longer, heat does transfer through vacuum via radiation. And no, you can't control the positions of the electrons to stop that radiation from happening, it is a quantum effect not something you can control.
Temperature and entropy are directly linked; it follows that temperature is also anthropomorphic. Although I think "observer-dependent" would be a better way to put it; it doesn't have to specifically be relative to a human.
https://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
Thermodynamics does have the concept of the entropy of a thermodynamic system; but a given physical system corresponds to many different thermodynamic systems. […] It is clearly meaningless to ask, “What is the entropy of the crystal?” unless we first specify the set of parameters which define its thermodynamic state. […] There is no end to this search for the ultimate "true" entropy until we have reached the point where we control the location of each atom independently. But just at that point the notion of entropy collapses, and we are no longer talking thermodynamics! […] From this we see that entropy is an anthropomorphic concept, not only in the well-known statistical sense that it measures the extent of human ignorance as to the microstate. Even at the purely phenomenological level, entropy is an anthropomorphic concept. For it is a property, not of the physical system, but of the particular experiments you or I choose to perform on it.