[oh_my_goodness]

Susskind says that entropy is determined by selecting a macro-state. He doesn't claim that the entropy of a macro-state depends on whether we know which macro-state the real system is really in.

If we happen to know, then, sure. For example we could pick a weird-ass observable state, and when we saw it we would know the entropy of the system was low. But the entropy of each macro-state just depends on how many micro-states we define it to contain. It doesn't depend on our knowledge of the system state.

[jbay808]

The concept of entropy wasn't invented so that we could calculate entropies of macrostates, it was so that we could calculate entropies of real systems and understand their behaviour. Macrostates are an accounting tool that helps us do this. You seem to be treating the calculation of macrostate entropy as an end-goal in itself, but also allowing yourself to somehow freely choose any macrostate you want. When it comes to applying thermodynamics in practice, you'll have to calculate the entropy of a real, or at least hypothetical, system.

The point of macrostates is that you ought to know which macrostate a given system is in. That's the thing that you know. You don't know which microstate it's in, but you do know which macrostate it's in.

For example, if I say "a cubic metre volume of air at room temperature and pressure", I've described a physical system. I've also described a macrostate.

If you're calculating the entropy of macrostates that are not consistent with a description of a system -- if you've defined your macrostates such that you don't know which macrostate a given system is in -- then in order to calculate that system's entropy you have to sum up over all such possible macrostates anyway, so you haven't saved yourself any work or earned any insights along the way.

So yes, you can calculate the entropy of a macrostate without knowing what macrostate a real system is in, but it kind of sounds like you're arguing that log(x) is not a function of variable x, because log(3) is a constant and log(4) is a constant, and you can divide up any x into constants of your choice.

[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.

[chermi]

I think you might enjoy cosma shalizi's paper "What is a macrostate?" https://arxiv.org/abs/cond-mat/0303625