[oh_my_goodness]

We seem to be stuck in a loop of explaining basic first-year statistical mechanics back and forth to each other repeatedly. I'm not sure why.

I'm making a pedagogical point. The OP addresses how difficult entropy is to understand. I'm responding to that. We don't need to talk about "knowledge" when you define entropy, or in an initial explanation of entropy. We could, but we could decide not to.

The log(x) example is a good one. First-time students who are learning about logarithms don't need to be told that a logarithm depends on 'knowledge' or on 'information.' It's ok to just tell them how logarithm is defined.

Sure, there is information. I'm saying it's confusing and unnecessary to introduce more big ideas like information, when the topic is "entropy is difficult to understand" or "logarithms are difficult to understand."

[jbay808]

Alright. I agree we seem to be stuck in a weird loop where we agree about all the observable facts but somehow are on different wavelengths in spite of that.

And I totally agree, entropy is a property of a macrostate. The information step comes inseparably in when you go from a system description to a macrostate. And you might just shuffle the confusion from not knowing what entropy is to not knowing what a macrostate is.

If you think it's clearer to teach students by explaining that the entropy of a macrostate is an objective property of that macrostate, that's fine. Just don't leave them believing that the entropy of a brick is an objective property of that brick.

[andi999]

Why shd the entropy of a brick not be an objective property (apart from a constant). I mean you can measure it, isnt it basically the integral of C/T dt?

[jbay808]

That would be a circular calculation, because the foundational definition of temperature is rooted in entropy: T = 1/(dS/dQ).

You can measure the temperature of a brick with a thermometer, but then you should understand what that thermometer is really telling you: https://bayes.wustl.edu/etj/articles/theory.1.pdf

And when you do that, you'll see why a thermometer doesn't do a good job of measuring the effective temperature of, say, a pumped laser crystal.