Comment by tsimionescu
Comment by tsimionescu 21 hours ago
But the point is that, regardless of how you choose to describe or even measure the system, it will need exactly as much heat to raise its temperature by 1 degree (or it will need as much kinetic energy to increase the average velocity of the constituents by the same amount, in the microstate framework). So there is some objective nature to entropy, it's not merely a function of subjective knowledge of a system. Or, to put it another way, two observers with different amounts of information on the microstate of a system will still measure it as having the same entropy.
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.