Comment by kgwgk
There is some objective nature to the operational definition of entropy based on an experimental setup where you fix the volume and measure the temperature or whatever.
And this is related to the statistical mechanical definition of entropy based on the value of the corresponding state variables.
But it’s not a property of the microstate - it’s a property of the macrostate which makes sense only in the context of the experimental constraints and measurements.
If we relate entropy to work that can be extracted someone with a better understanding of the state of the system and operational access to additional degrees of freedom can extract additional work.
Thermodynamics assumes the state variables provide a complete description of the system. Statistical mechanics assumes the state variables provide an incomplete description of the system - and work out what that entails.
> But it’s not a property of the microstate - it’s a property of the macrostate which makes sense only in the context of the experimental constraints and measurements.
The same can be said about the wavefunction then, right? You can't directly observe it, you can only use it to predict the statistics of a particular experimental setup. So, at worse, entropy is as real as wavefunction amplitudes.
> If we relate entropy to work that can be extracted someone with a better understanding of the state of the system and operational access to additional degrees of freedom can extract additional work.
Is this actually true? Per my understanding, if I give you three containers, two of which are filled with some kind of gas that you know nothing about, and the third with a mix of those same gases, you can measure their entropy using thermodynamic experiments and tell which of the three is a mix of the other two because it will have a higher entropy. So, you can extract more work from one of the boxes despite not knowing anything more about it.