Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Entropy and states of matter



Regarding:
...
Couldn't one argue that the surface energy *is* extensive as it does scale
the same as the size of the two dimensional manifold on which it resides?
Double the surface area, you double the surface energy.

Sure. If our system of interest is only the 2-d world of one of the
crystal faces then for that system the surface energy is extensive
over that 2-d face. But if, as I supposed, that the system of
interest is the crystal itself, then the surface energy is not
extensive for that other bulk system.

I suppose this is quibbling over the definition of "extensive" ...

Exactly. Joel has a valid concept. We just need to
straighten out the nomenclature.

Usually when people say "extensive" it is assumed to
mean regular D=3 extensive. If you want to talk about
something that is D=2 flatland extensive, you need to
say so explicitly. That's all.

This looks like a good way to handle the situation.

BTW, besides the previous argument that I gave with the crystal
surface that argued the claim that infinite divisibility did not
necessarily imply (bulk) extensiveness, a little more thought has
just about also persuaded me that the concept of extensiveness does
not necessarily entail the concept of infinite divisibility either.

To see why, consider a system that has some relevant quantity that is
quantized and whose quantum chunk size for that quantity is not
infinitesimal *at* the level of description for which we want to
describe our system. Such a quantity is not further divisible beyond
the finite and relevant chunk size. But this quantity can still be
asymptotically extensive in that the total amount of that quantity
scales proportionally to the volume on scales much *larger* than our
scale of description. In essence the concept of infinite
divisibility refers to our ability to go much further *down* in scale
size before encountering any graininess for our quantity. But the
concept of extensiveness refers to the ability of our quantity to
accumulate additively on ever *larger* length scales. These two
concepts appear to look in opposite directions of scale from the
convenient scale size unit of our quantity for our system at hand.

David Bowman