Re: [Phys-l] Gibbs paradox

[Carl Mungan <mungan@usna.edu>]

> To summarize:  It appears that one of the central claims is
> that when we take two samples of distinguishable particles
> and mix them, the entropy is additive.  This claim cannot
> withstand even the slightest scrutiny.

I'm not sure who claimed that. For myself, I hope the answer is that 
if you mix them, the entropy increases by the entropy of mixing.

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?

> This is not a big deal.  The energy is not quite extensive,
> because of surface-tension and surface-reconstruction effects,
> and this has not caused the world to end.  Discovering that
> the entropy is not quite extensive will also not cause the
> world to end.  For large systems, the correction terms will
> be insignificant ... but they exist in principle and they
> are significant for small systems.

Yes, I believe those are exactly the kinds of examples Swendsen had 
in mind. -Carl
--
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/