Re: [Phys-l] Gibbs paradox

[John Denker <jsd@av8n.com>]

On 04/01/2011 09:33 AM, Carl Mungan wrote:
> I think the question of additivity is if you *don't* mix them. Take 
> two identical copies of the system (say your two sets of decks, each 
> individually shuffled), put one on top of the other but don't 
> reshuffle (in the gas case, that would mean keep a partition in 
> place), and now ask: what is the entropy of this new "doubled" system?


If that's the question, I'm more confused than ever as to what 
this thread is about.

a) There is a theorem that says that if the two subsystems have
 independent probabilities, the entropy is additive.  This isn't
 even physics;  it's just mathematics.  You can prove it on the
 back of a post-it note.

b) If we don't mix them, it cannot possibly matter whether they 
 are identical or distinguishable.

What am I missing?