Comment on Entropy and Temperature

Fri, 19 Dec 2014 22:35:49 GMT

Omega tells us the state of the water at time T=0, when we put the beer into it. There are two ways of looking at what happens immediately after.

The first way is that the water doesn't flow heat into the beer, rather it does some work on it. If we know the state of the beer/water interface as well then we can calculate exactly what will happen. It will look like quick water molecules thumping into slow boundary molecules and doing work on them. This is why the concept of temperature is no longer necessary: if we know everything then we can just do mechanics. Unfortunately, we don't know everything about the full system, so this won't quite work.

Think about your uncertainty about the state of the water as you run time forward. It's initially zero, but the water is in contact with something that could be in any number of states (the beer), and so the entropy of the water is going to rise extremely quickly.

The water will initially be doing work on the beer, but after an extremely short time it will be flowing heat into it. One observer's work is another's heat, essentially.

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