[im3w1l]

I've been trying to reconcile these perspectives, and I think it really is both. And they are both physically relevant.

Consider the subjective entropy perspective. If you know the exact microstate of a system, then you can in theory play the part of Maxwell's demon. You could have a little gate that you open only for fast particles, and using your knowledge of the microstate, you can predict exactly when they will arrive.

But consider the objective perspective. If you take this very same system and put it in thermal contact with another system, then an objective entropy perspective is the relevant one. Those systems will equilibrize and your subjective knowledge is irrelevant to that process.

I haven't fully wrapped my head around it yet, but I do think that acknowledging both is a step in the right direction at least.

[jbay808]

> If you take this very same system and put it in thermal contact with another system, then an objective entropy perspective is the relevant one. Those systems will equilibrize and your subjective knowledge is irrelevant to that process.

The subjective view handles this scenario just fine, though, and makes more accurate predictions than the objective view.

For example, there are systems where some aspects of the original microstate survive thermal contact with another system. We use such systems to store data! I bet your hard drive is in thermal contact with its environment right now! It's very hard to reconcile this with an objective take on entropy.

And there are some systems that will rapidly be scrambled. The subjective perspective has no problem admitting that your knowledge of a system can become inaccurate and useless. Even without thermal contact, you'd need to perform a tremendous amount of (perhaps reversible) computation in order to make a functioning Maxwell's demon with your initial microstate conditions, because the microstate will evolve in time in a complicated way. The subjective view is still totally consistent with entropy of a system increasing over time!

[im3w1l]

I wrote two replies to this that I both deleted. Then I had a good long thunk, and here's what I came up with.

The temperature of an object can be determined through 1/T = dS / dE. What is this S? How can it exist if you know the system perfectly? And here is where the great insight comes. The thermometer! You apply a thermometer to a system you perturb it! The system may have started in one particular microstate, but the very nature of thermal contact involves random influence. Those random tiny influences from the thermometer allow the object (harddrive in our case) to enter a bunch of microstates with certain probabilities. And that's what S measures.

So our subjective knowledge does actually not matter. (Classically speaking) the system is in a particular microstate we may know it or not, and it still manages to have a temperature. That is due to the states it could hypothetically enter (but haven't yet)!

If we think back to the harddrive and it's contents: Very gently touching a harddrive with a thermometer while not scramble its contents. So we may say that microstates corresponding to different files than the ones you put there are actually not accessible. And they don't contribute to the entropy we used for the temperature.