4 ms·

>You are unable to explain how reducing the space occupied by the initial configuration you proposed could change the temperature - which you say is 0 in all th

>You are unable to explain how reducing the space occupied by the initial configuration you proposed could change the temperature - which you say is 0 in all those cases - or the macrostate - which you call absolute zero macrostate in all those cases. The entropy would be the same whenever the particules are more concentrated than in your example - even though they would have lower probability of ocurrence. Don't you agree? You're unable to read my explanation which i've already repeated twice. Go back and look it up. I even went with your cubical definition. I don't agree. Entropy is lower when the current macrostate has a low probability of occuring. >There is no entropy of the microstate - the entropy depends on how you decide to define the macrostate The macrostate is defined in terms of possible microstates. Thus Entropy relies on both microstate and macrostate. >If by sheer luck all gas particles moved to the exact left side of the container the energy wouldn't change, the macrostate wouldn't change, the entropy wouldn't change - it doesn't matter how unlikely that is. Wrong. Energy wouldn't change. Macrostate changes. Entropy changes. >It doesn't matter if you know the position of each particle. The entropy for the thermodynamical system described in the previous paragraph is independent of your knowledge of where the particles are or how unlikely you think their positions are. Isn't this my point? And weren't you against my point? Now you're in agreement? My point was entropy is independent of knowledge. Your point was that it is dependent. >I agree that you could use alternative ways of defining the macrostate where that happens! (And calculating Gibbs entropy will give different results. One can even get zero entropy using the microstate as macrostate - and one may actually want to do that if the microstate is known!) Except you don't have to do this. My point remains true given MY stated definitions of macrostate. >Both concepts are used. When you say that the equilibrium is simply the highest entropy state but the equilibrium entropy can also be lower I'm not sure if it can be read as one of those or you're saying something else entirely. I made a true statement that from what I can gather you agree it's true. You're just trying to extrapolate my reasoning behind the statement. It's pointless. Example: If I give you a number, say -1, do I mean i^2 or 0 - 1? because one of those equations is impossible to express in reality.

kgwgk 4y ago
>>If by sheer luck all gas particles moved to the exact left side of the container the energy wouldn't change, the macrostate wouldn't change, the entropy wouldn't change - it doesn't matter how unlikely that is. > Wrong. Energy wouldn't change. Macrostate changes. Entropy changes. That's my thermodynamical system - that I decided to describe using the state variables N, V, E. S_kgwgk = constant I have agreed that you can chose to define macrostates as you wish! (You cannot measure them though. You don't have access to my system. They are purely hypothetical.) And then you can say things like "If the position of the particles in your system is X, S_deltasevennine = whatever." Hopefully you will agree that someone else could choose to define the macrostate differently and say things like "If the position of the particles in kgwgk's system is X, S_anon = somethingelse." Let's imagine that the position of the particles is actually X. What is the entropy of the system then? S_kgwgk? S_deltasevennine? S_anon? They are all different! If you think that you can define macrostates for my system in some arbitrary way (your own words: "I'll choose something arbitrary.") and others can't - or that yours are somehow more real - I really wonder why. And as I said, someone could also come and say "If the position [and velocities] of the particles in kgwgk's system is X, S_vonneumann = 0." [a complete definition of the microstate requires knowing both position and momentum - there might have been some ambiguity about that before but it shouldn't distract us from the main points]
- deltasevennine 4y ago
  I thought we agreed on my definition. If you want to make your own definitions of macrostate sure. No rule against that, I just don't see your point. >If you think that you can define macrostates for my system in some arbitrary way (your own words: "I'll choose something arbitrary.") and others can't - or that yours are somehow more real - I really wonder why. I really wonder why you even say this. Anyone can make up a macrostate we just choose to agree on one for discussions sake. But in the real world things like pressure and temperature are some universal agreed upon ones. I simply made one up so we can center our discussion around it and you took it into other territories. You can switch up definitions all you want. But no matter your definition of macrostate, this remains true: Entropy is independent of knowledge. Your initial argument was against that. I haven't seen you make any argument in your own favor. Just side discussions on who's definition of macro state to use.

kgwgk 4y ago

>>If by sheer luck all gas particles moved to the exact left side of the container the energy wouldn't change, the macrostate wouldn't change, the entropy wouldn't change - it doesn't matter how unlikely that is. > Wrong. Energy wouldn't change. Macrostate changes. Entropy changes. That's my thermodynamical system - that I decided to describe using the state variables N, V, E. S_kgwgk = constant I have agreed that you can chose to define macrostates as you wish! (You cannot measure them though. You don't have access to my system. They are purely hypothetical.) And then you can say things like "If the position of the particles in your system is X, S_deltasevennine = whatever." Hopefully you will agree that someone else could choose to define the macrostate differently and say things like "If the position of the particles in kgwgk's system is X, S_anon = somethingelse." Let's imagine that the position of the particles is actually X. What is the entropy of the system then? S_kgwgk? S_deltasevennine? S_anon? They are all different! If you think that you can define macrostates for my system in some arbitrary way (your own words: "I'll choose something arbitrary.") and others can't - or that yours are somehow more real - I really wonder why. And as I said, someone could also come and say "If the position [and velocities] of the particles in kgwgk's system is X, S_vonneumann = 0." [a complete definition of the microstate requires knowing both position and momentum - there might have been some ambiguity about that before but it shouldn't distract us from the main points]

deltasevennine 4y ago
I thought we agreed on my definition. If you want to make your own definitions of macrostate sure. No rule against that, I just don't see your point. >If you think that you can define macrostates for my system in some arbitrary way (your own words: "I'll choose something arbitrary.") and others can't - or that yours are somehow more real - I really wonder why. I really wonder why you even say this. Anyone can make up a macrostate we just choose to agree on one for discussions sake. But in the real world things like pressure and temperature are some universal agreed upon ones. I simply made one up so we can center our discussion around it and you took it into other territories. You can switch up definitions all you want. But no matter your definition of macrostate, this remains true: Entropy is independent of knowledge. Your initial argument was against that. I haven't seen you make any argument in your own favor. Just side discussions on who's definition of macro state to use.