Statistics, Thermodynamics and Single Atoms

I recently asked a question in here about whether thermodynamics applies to
individual atoms. The gist of the response as I understood it was that
thermodynamics applies only statistically to groups of systems or to very
complex systems. But the more I was thinking about it the more I was still
confused, because we use statistics to understand even a single atom, eg.
the likelihood of finding an electron in a given position. So if we
understand single atoms by means of statistics, why doesn't thermodynamics
apply to single atoms which are after all very complex systems? Why don't
atoms wear down and stop their dynamic activity?

<[Only registered users see links. ]> wrote:

Erwin Schrodinger came up with his famous wave equation, but waves are
always displacements in some medium (air, water, the electromagnetic field,
etc.) and this raised the question as to what is 'waving' in the Schrodinger
equation. Max Born postulated that what is waving is the probability of
finding the quantum system is a particular state. Since probabilities in
classical physics are always related to epistemic constraints (i.e. how much
we can know about a system given that we can't be in possession of *all* the
details) this raised the further question as to whether probabilities are
irreducible in QM (i.e. there are no further details) or are symptomatic of
some deeper detail to which we don't (yet?) have access. The latter scenario
is known as the "hidden variables" hypothesis. If the hidden variables
hypothesis turned out to be the case then it may open the door to some kind
of thermodynamics analogy on the quantum level, but John Bell attempted to
establish mathematical support for the hidden variables hypothesis and wound
up causing problems for such an hypothesis. His theorem was subsequently
tested by Alain Aspect et. al. and the results supported his conclusions
(i.e. that there are no *local* hidden variables). This points up the
radical difference between classical systems and quantum systems, and is
known as non-locality. David Bohm, however, was not convinced that every
kind of hidden variable hypothesis was now defunct, and proposed one such
scheme that evades Bell's conclusions. His ideas, however, fall foul of
Lorenz invariance, and so are not received well by many physicists. If I'm
mistaken about any of this then I'm sure I'll benefit from the comments of
others in this group more knowledgeable than myself.

Dear dougwedel:

<[Only registered users see links. ]> wrote in message
news:3jNCf.19573$[Only registered users see links. ].prodigy.ne t...

No. "Statistically large" is different than "complex".


Let's see "position" requires space... a statistical construct.
"Energy" requires space and time... yet more statistical
constructs.

Yes you can "screw" the large statistical constuct called "the
Universe" into the problem of a single atom, but you get only
probabilites as a result.


We don't. We understand populations of them.


No. A single atom does not live by the laws of thermodynamics,
especially the second law.


Answered.

David A. Smith

<[Only registered users see links. ]> wrote in message
news:3jNCf.19573$[Only registered users see links. ].prodigy.ne t...
to

correct.


Not to 'very complex systems' per se, but the operation of a system over a
large number of trials can be treated statistically.


Think about exactly what we are describing in each case.

In the case of a single atom QM gives us the *probability* of finding an
electron at a specific location in relationship to the nucleus (or the
nuclei of a molecule or a molecular ion). A specific mathematical treatment
of the wave function of a single electron gives us the chance that it would
be at a specific place in the atom, *IF* we happened to look there fore it.
Sometimes it will be there and sometimes it won't. It is mathematically
analogous to the problem of "If I flip a coin once, what are the chances it
will come up heads?"

In the 'thermodynamic' case of a large number of identical systems
statistics gives us the average values of measured quantities made over all
of the systems. If we make the same measurement (i.e. kinetic energy) on
*ALL* the systems and THEN find the average kinetic energy per system, that
would give us the 'temperature' of the entire collection. This is
mathematically analogous to the problem of "If I flip a million coins once,
how many of them will come up heads?"

The third case, that of a system examined over a large number of trials, is
mathematically analogous to the problem of "If I flip one coin one million
times, how mamny of them will come up heads?" This is time consuming and
usually done only in particle physics labs wherein a large number of trials
with identical systems are carefully examined individually. These
experiments can take *YEARS* to complete.

There are significant differences, but all the problems are closely related.


Tom Davidson
Richmond, VA