Russ Abbott wrote circa 07/20/2010 09:55 PM: > If all the particles were arrayed in a regular lattice, the description > could be smaller than the universe itself. I thought that was the point > of entropy.
Perhaps you're right. But that is also counter-intuitive to me. If entropy really is a measure of "disorder" in any sense, then it's hard for me to imagine a maximal entropy state as describing a completely smooth landscape where every element sits on a point in a regular lattice. But physically, entropy is about the ability to do work. So, it seems to me that our understanding of the concept of "heat death" needs a little more emphasis on "heat", which describes the vibration of particles and says nothing about any microscopic patterns. A heat death doesn't describe particles laid out on a regular lattice. It's about not being able to _use_ any of the microscopic activity, whether you know what that activity is (data about the degrees of freedom for every particle) or not. Still, a shortest description of it can be made by uniform RNGs over all the potential degrees of freedom for elements spread more or less evenly, though not necessarily _totally_ ... omnisciently, god-like, regular lattice evenly, through the universe. In order to get that short description, though, you have to abstract yourself from the microscopic detail. The RNG distribution demarcates the ontological wall, behind which we're completely ignorant (e.g. "heat"). A fully concrete, non-abstract model would be the same "size" as the universe itself, even in heat death. > This is a perspective from outside the system, > but it would seem to be a perspective in which entropy makes sense > without having to say anything special about an observer. Of course > whenever we say anything about anything there is an implied observer, > but we don't complain about that in other contexts. I don't see how it's possible to talk about a perspective from outside the system without talking about an observer, even if that observer is just another, separate, system. That was the whole point. Entropy only seems like a coherent concept in the context of 2 or more systems, making either extreme (heat death of the universe or all matter inside a singularity) degenerate cases. -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
