I think the issue is more with your understanding then my explanation.
>What do you think is the definition of macrostate?
We first introduce the very fundamental statistical ideas of microstates and macrostates. Given a system (e.g., a gas), we view it as built from some elementary constituents, (e.g., molecules). Each constituent has a set of possible states it can be in. The thermodynamic state of the system (which characterizes the values of macroscopic observables such as energy, pressure, volume, etc. ) corresponds to many possible states of the constituents (the molecules). The collection of states of all the constituents is the microstate. To keep things clear, we refer to the macroscopic, thermodynamic state as the macrostate. The vast disparity between the number of possible macrostates versus microstates is at the heart of thermodynamic behavior! The number of distinct microstates giving the same macrostate is called the multiplicity of the macrostate. The multiplicity is a sort of micro-scopic observable which can be assigned to a macrostate.
>The standard notion in statistical mechanics is that if we have, for example, a volume of gas in equilibrium at (constant) ambient temperature and we measure the pressure it doesn’t change. The macrostate doesn’t change. That’s what being in equilibrium means. The macrostate is in that case defined by the variables P,T,V. If all you knew was the value of these three variables and they didn’t change how could the macrostate - or the entropy - change?
This notion is wrong. It CAN change. It just has an extreme low probability of changing from equilibrium to some low entropy state. The probability is low enough that you practically don't need to consider it, but you must consider it from a technical standpoint.
If by sheer luck all gas particles moved to the exact left side of the container. My measurement tool (thermometer) for macrostate was on the right side of the container then it registers zero. There is nothing in the laws of physics that prevents this from happening. Only probability makes this situation unlikely to happen.
>You tell me that if you know the precise position of the particles of that gas then the macrostate and the entropy change all the time.
No. I'm saying that the temperature reading on the thermometer a macroscopic measurement is INDEPENDENT of knowledge. Your mind doesn't control microstates and thus the macrostate of the system.
>But you also tell me that “Knowing more or less about a system does not change it's entropy.” Which is in flagrant contradiction with the two previous paragraphs.
Flagrant? You're offended? Well you can leave if you're offended. Using words like this also Offends me so we can end the conversation.
