Re: errata- Max entropy

["Rauber, Joel Phys" <RAUBERJ@mg.sdstate.edu>]

Gang,
> > The statistical underpinnings of the 2nd law of thermodynamics do not 
imply
> that the >entropy of an isolated system increases or stays the same for any
> given process.  It is >possible for an isolated system, through spontaneous
> fluctuations, to have a lowering >of its entropy.
>
> and below has a serious confusion.  Everywhere where I refer to an isolated
> system, I should have said a system held at constant temperature by means 
of
> being in thermal contact with a reservoir at that temperature.
>
> i.e. I was thinking in terms of a canonical ensemble, but wrote a
> description of a system best interpreted in terms of a micro-canonical
> ensemble.

> > What could possibly be the meaning of the entropy of *a* system which
> > is a member of a canonical ensemble? Are you suggesting that the
> > canonical ensemble is not itself a representation of *a* system?


I simply mean that one is using the formalism of the canonical ensemble to 
analyse
some physical system.  In that context the physical system could be viewed 
as a
representative member of the ensemble.

> I didn't comment on your earlier posting because I believe that there
> is little meaningful content in the concept of an "instantaneous value
> of the entropy of a system".

Please expand on this, I suspect you have in other threads previously; but 
alas, an educators job is never finished and much like Sisyphus, one is 
doomed to repetition.

Do you prefer to compute an average value of entropy for a system?  I have 
trouble understanding the 2nd law statement that entropy never decreases for 
a process; unless I can view it as a calculatable quantity that evolves in 
time.  Which I interpret to mean that I can calculate it, given enough 
mathematical prowess, at some instant of time.

> Since so few seem to understand the
> meaning of entropy in a sytem in thermodynamic equilibrium there is
> insufficient context to make the more arcane concept meaningful.

Since I wished to view systems in the context of thermodynamic equilibrium, 
I needed to view the system in terms of the canonical ensemble.

My point is something that I have always found fascinating.

On the one hand, you have the impressive edifice of Thermodynamics (recall 
Einstein's quote that Thermodynamics is probably the one edifice that will 
stand the test of time, unchanged).  And this edifice has the 2nd law, hard 
fast and immutable; engraved on tablets of stone: The entropy of a system in 
equilibrium does not decrease.

On the other hand, following Boltzmann and Gibbs; we have the statistical 
mechanical underpinnings of Thermodynamics and you find the idea of 
fluctuations of quantities; implying that the entropy can over some periods 
of time decrease.

This apparent? conundrum?, I find alluring and is a factor in how I came to 
be stuck in a career in physics.

> If the microstate of any system is known to be any quantum mechanical
> eigenstate whatever then the entropy of that system is simultaneously
> zero and meaningless!

And if its not known to be in some specific eigenstate?

> Chew on that one a bit.

Chomp, chomp, chew,chew,  I always find there to be a lot of gristle in 
thermodynamics and statistical mechanics.

Joel