To say "all the stars would eventually burn out" is a semantic stumbling block,
apparently. There will come a time -- eventually -- when stars no longer form
from the gasses remaining from previous stars [so the theory goes].
I suggest that the most important point is that none of this will happen
suddenly, even on a cosmic time scale. The stars that will form from
interstellar dust and gasses will be ever smaller and cooler; and eventually
will fail to go thermonuclear.
It is also worth noting how matter changes state at temperatures very close
to absolute zero. In this state, called a Bose-Einstein Condensate, the
"particles" in an atom become very diffuse, ie. much less localized, and in
fact much less disinct, to the point that there can not be said to be a
proton and an electon in the hydrogen atom, but simply, a hydrogen atom in
the Bose-Einstein state. Presumably, at the "end" of the universe, all
matter has reached this state, and no further diffusion or cooling is
possible. (This is, of course, assuming an open universe.)
(
Short description of Bose-Einstein Condensation:
http://128.178.177.16/ene/ene_aug95_walraven_text.html#gen1
The Bose-Einstein Condensation Homepage:
http://amo.phy.gasou.edu/bec.html/
)
-- John Porter jporter@btg.com