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Re: ENERGY WITH Q




On Mon, 29 Oct 2001, John S. Denker wrote:

Any energy change in a system that is associated exclusively with
an alteration in the occupation numbers (rather than the energy
levels) of the allowed quantum states *will* alter the entropy
of the system and ought, therefore, to be considered "heat."

I don't get it.

How are we going to change the entropy without changing the
energy (at any
nonzero temperature)?


I didn't quite understand the comment either, as it seems that one
changed
the energy by changing the occupation numbers?

If I might interject, I think I know where the misunderstanding is...

Consider a specific example - a standard quantum mechanical 3D box with
some specific size, and hence specific energy levels. Add several
particles at equilibrium inside. The average occupation of each level will
be a well established number.

If we raise the average energy of the particles, the the energy levels are
unchanged (set by the size of the box) but the particles will on average be
in higher levels. This change is "associated exclusively with an
alteration in the occupation numbers (rather than the energy levels) of the
allowed quantum states". It is not that there is no change in _energy_,
but rather that there is no change in the allowed _energy levels_. So this
is "heat" (based on the original premise).

If we decrease the size of the box, adiabatically compressing it, the
occupation number of each state will remain constant, but the energy of the
specific states will be higher (because the box is smaller). This change
is "associated exclusively with an alteration in the energy levels (rather
than the occupation numbers) of the allowed quantum states". So this is
"work" (based on the original premise).

It seems like an interesting way to define heat and work, although it is a
little beyond most beginning students. It seems you have to understand
quantum statistical mechanics before you can do thermodynamics.

Tim Folkerts