> Note that I was the first one to propose a particular way to define the macrostate (energy) of the system to understand what you meant. Your reply was "that's not the definition of macrostate. It's just one arbitrary choice you have chosen." And you gave your own arbitrary choice "I'll choose something arbitrary. Temperature as measured by a thermometer".

No. You explicitly ASKED for my definition, then I said that.

When I said that's not the "definition of macrostate" I did not make an arbitrary choice there. I simply stated that IF you think energy was the definition of macrostate, then you are wrong.

> Maybe be can agree that [Gibbs] entropy [which is a property of the distribution of microstates corresponding to our description of the system based one some macroscopic properties] is independent of knowledge [other than about that particular macroscopic description].

This is the point of the ENTIRE thread starting from your INITIAL reply. Technically this argument is over. You weren't in agreement with me, now you are, so you were wrong and I was right. This sentence admits that.

The rest of the stuff here is side tangents and it's hard to see the main point. I can entertain it though for a little bit but this here is essentially the end.

>The discussion started with me trying to understand what did you mean by "low entropy" when you said:

This discussion started with you saying that if I know the microstate of the system entropy is zero. If you wanted to understand What I thought about "low entropy" then this was NEVER stated. The thread is based off what is stated and what is not stated. It is not based off of what your internal thoughts and intentions are. If you want the topic to based off your own thoughts, they need to be expressed explicitly in statements. You did so just now, but way too late.

>Note that if for some reason all the particles in the gas go away from the thermometer for a second the temperature of the mercury won't change (ignoring that it will radiate energy over time). The reading of the thermometer doesn't drop to zero just because there is nothing there.

This is pedantic. Obviously. I can take it into account. Let's say the greatest average speed measured of a particle and the time it takes for a particle at this speed to travel across the box is the time it takes for the thermometer to drop to zero degrees from the maximum temperature. It's quite fast but particles within the vicinity will keep the mercury level stable but if they were concentrated in a corner, the mercury drops fast enough to change the reading of the thermometer.

>Let's assume that you are somehow measuring the temperature in a small region somewhere with a very high reaction time. What you measure will not depend in any way on the particles that are elsewhere. The particles in the rest of the box could be well spread or all near one corner and you would have no reason to say that the latter configuration is lower entropy than the former based on your macrostate.

I specifically defined it as a thermometer to make location matter. Switching the location of the thermometer is switching the definition as well.

I really don't see what your point is. You think I'm wrong about something? What am I wrong about?

>But at some intermediate point the reading of the thermometer will be the same as in equilibrium. Your macrostate will be the same as in equilibrium. Your entropy will not be lower than in equilibrium. Even though you said -if I understood you correctly- that the entropy should be lower because the higher concentration has a lower probability of occurring.

Your point seems to be buried in here somewhere and I can't parse it. There is a macrostate that is equilibrium, yes.

Are you referring to mercury level mid transition? This is pedant-ism to the max if you are. Yes the mercury level will display the WRONG temperature if it's mid transition. Not willing to constantly adjust the model to little flaws you find. Last time: Let's switch to a digital thermometer that displays temperature at time intervals that are equal to the length of time it takes for the maximum speed particle to travel across the box. There is no transition value now. All temperature readings reflect an instantaneous observed truth at an instantaneous point in time, but that temperature is displayed at non-instantaneous intervals.

It also seems to me that your definition of macrostate is meaningless. The total energy of the universe is hypothetically the same all the time. If the macrostate was just energy there's no point to it, because entropy would then be an unchanging constant.

I think we're done here. I'm just trying to guess what you're driving at. You'll need to clarify your point if you want me to continue. What exactly are you trying to say here?