Re: Entropy, Objectivity, and Timescales

[jmclean@chem.ucsd.edu (James Mclean)]

DSCHROEDER@cc.weber.edu says:
> > Take the initial quantum state, and propagate it with the Schrodinger
> > eq. until there is a non-zero probability of finding the system in each
> > state considered to be accessible.  Does that work for everyone?
>
> No, doesn't work for me.  Let's assume that our system is isolated,
> and use a basis of stationary (definite-energy) states.  Then the
> Schrodinger equation predicts that only those states that appear
> in the initial wavefunction (decomposed in this basis) will ever appear
> in the wavefunction in the future.  Thus, you can wait as long as you
> like, but the number of "accessible" states (counted in this way) will
> never increase.

Maybe it's my turn to be obtuse, but isn't this just energy conservation of
an isolated system?  If the system is isolated, then the energy is
conserved, so the thermodynamically accessible states are exactly the ones
which are allowed by the quantum mechanics, no?

(By the way, I don't understand Leigh's reluctance to assume an isolated
system.  That assumption seems to occur extremely frequently in statistical
mechanics, as I recall.  Perfectly rigid walls and perfectly insulated
walls are everywhere you turn.)

> > What James means is that we express our microstate as a combination of
> > single system states (e.g. particles in a box of gas) and allow them to
> > interact. The propagation of the interaction then proceeds at some
> > finite speed near sound speed.
>
> So instead of a basis of exact stationary states for the whole system, 
> you'd prefer to use a basis of products of single-particle states.
Leigh is very generous in his assumptions as to how much I've thought about
this :-).
But I just thought I would add that "products of single-particle states"
are a little dangerous.  I just read a recent AJP article (sorry, don't
have the reference) about how at STP, the vast majority of "products of
single-particle states" are dissallowed by the Pauli principle (for
fermions).  The article goes on to show how the statistical mechanics still
works even after making this grossly erroneous assumption.

-- 
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry