Tristan L 2 Posted June 4 (edited) 7 hours ago, studiot said: I was hoping to introduce this in a more measured way, but you have jumped the gun I didn't and don't want to do that; rather, I only wanted and still want to make sure that there are no misunderstandings before I answer your other points and go on with the discussion. 7 hours ago, studiot said: I am not, and never have, disagreed with your outlining of basic mathematical set theory in respect of the word 'partition'. The important thing is that in this whole thread, I have only ever talked about partitioning the set of microstates into macrostates, not partitioning the system into subsystems. However, you seem to imply that I have done the latter by saying 21 hours ago, studiot said: For the subsytems (partitions in your parlance) In reality, I have only ever talked about partitioning the phase space. 7 hours ago, studiot said: Mathematical partitioning of Mi (is based on) equipartition and implicitly assumes the 'equipartition theorem' of thermodynamics. In what way does it do that? Does that mean that without the equipartition theorem, one microstate could belong to more than one macrostate? 7 hours ago, studiot said: You have also mentioned disjoint partitions, which is important in the mathematical statistics of this. What exactly do you mean by that? All members of a partition are pairwise disjoint by definition. Being sets, some partitions P, Q are disjoint (share no common subsets of the ground-set), while others are not. 7 hours ago, studiot said: Nor can it arise in information technology, whose partitions are disjoint. Partitions of what? 7 hours ago, studiot said: Finally, I do hope, you are not trying to disagree with Cartheodory. Of course not, but as I said, I want to do away with any misunderstandings on my or your part before talking about your other points, including Caratheodory. 7 hours ago, studiot said: And you seem to be disagreeing with my classical presentation, because it is much shorter than the same conclusion reached in the statistical paper you linked to ? Actually, I linked to the paper mainly because I find it interesting that there may be a way to outsmart the Second Law 😁. Edited June 4 by Tristan L 0 Share this post Link to post Share on other sites