[kgwgk]

>>I thought we had agreed that entropy is something you calculate with a model,

>We did agree. I never said otherwise. Where are you getting this idea? I'm saying our agreement on this fact is useless. Why don't you actually fully read what I wrote.

It was a minor correction. I wouldn't say that entropy is a "model". But essentialy we agree, that's what I meant. We agree that we agree!

>> I was trying to say that the inputs to S(...) are the things that we know because we did measure them or set their values. It seems that we agree on that because it's extremely obvious.

> I spent paragraphs remarking on this ALREADY.

Again, I was stressing that we had also reached a clear agreement on that point. (Except that I don't know what do you mean by me implying something about "some input parameter modeled after knowledge" if every input corresponds to knowledge and that's a pointless thing to discuss.)

> The Macrostates don't change based off your knowledge. You choose the one you want.

And if you want, you can choose a new one when your knowledge changes! One that corresponds to everything you know now about the physical state. Then you can do statistical mechanics over the ensemble of states that may be the underlying unknown physical state - with different probabilities - conditional on everything you know. In principle, at least.

[it was an interesting discussion, anyway]

[deltaonefour]

>Again, I was stressing that we had also reached a clear agreement on that point.

And I'm stressing the agreement was pointless and even bringing up the fact that entropy is a model doesn't move the needle forward in any direction. You haven't responded to that. I still don't understand why you brought it up. Please explain.

I also don't understand how zero knowledge of the input parameter applies as well. This argument works for every model in existence and is not unique to entropy. Again not sure why you're bringing that up. Please explain.

[kgwgk]

I never said it was unique to entropy. (And i still don’t understand if there some meaning that escapes me in calling entropy a “model”. Are temperature and pressure also “models” or is it unique to entropy?)

If I have a system in thermal equilibrium with a heat bath and know the macrostate P,V,T I can calculate the energy of the system only as a probability distribution - it’s undefined. If I knew the state precisely I could calculate the exact energy of the system.

If I define lycanthropy as “error in the determination of energy” it’s positive given the macrostate for the system in a heatbath and zero given the microstate of the system. Of course, given the microstate one can know the energy but can also pretend that the energy is still indeterminate.

While the distribution of energies - and the whole thermodynamical model - may still be useful its meaning would change. It would no longer be the most complete description of the system that encodes what can be predicted about it. Of course if that was never the meaning for you, you’ll see no loss. But I thought we were talking about physics, not mathematics. The meaning of thermodynamics is a valid point of discussion. The interpretation of the second law remains controversial.

I think this discussion has run its course - I may no longer reply even if you do. Thank’s again, it was interesting.