Re: Entropy, Objectivity, and Timescales

[Leigh Palmer <palmer@sfu.ca>]

David Bowman has weighed in. He didn't pick up on the fact that
the thermodynamics course description  was for a course given by
Dan, not by me. SFU has two courses, one at second year level in
classical thermodynamics and one at third year level in
statistical physics.

I find it astonishing that so much talk of quantum mechanics is
introduced here. The classical entropy is very easy to
understand. Sure, it's difficult for students to understand it
at first, but they eventually get it.

This is tiresome, but...

> Ok, here's my next reply to Leigh...
>
> > Dan says (and I omit much I do not choose to argue further)...:
>
> In other words, you're refusing to answer some of my honest questions.
> I still want to know precisely how large a system has to be before
> we're allowed to talk about its entropy.  I've now asked you three
> times.

I've heard it said that there is no such thing as a stupid question.
I can now adduce this as a Gegenbeispiel. If you do not know the
answer to this question look in your course description. The answer
is that there is no precise size to a system which can be treated
thermodynamically. Surely you must know that!

> Look, I don't want to argue quantum mechanics here.  But I've never
> before heard anyone claim that you need to understand quantum
> indeterminacy to understand entropy.

You don't have to know anything about quantum mechanics to understand
entropy. It can be understood entirely as a macroscopic classical
phenomenon.

> I'm honestly not sure what "the authoritative view of entropy" is,
> nor do I believe that the question should be decided by appeal
> to authority.  Please read what I said.  I'm making no claims
> about your intelligence.  I'm simply countering your implication
> that all the authorities are on your side.

What does Rudolf Clausius say? He invented the concept. Boltzmann
and Gibbs seemed to understand it. What authorities are on your side?

> For the record, I am neither a creationist nor a postmodernist.

As I've pointed out before, few physicists are. I certainly don't
know any holding either delusion. Most of us can be characterized
as atheists (according to the article cited earlier) and I would
guess that a majority of us are also objective realists. If there
are some of us who are not reductionists then some of us practice
what we don't believe, but "holism" (the opposite of reductionism
in modern parlance) yields no practical result other than to
"explain" inability to do mechanistic calculations.

I wish to point out that point of view plays a very important role
in physics. Understanding the philosophical orientation of a
colleague is central to understanding what he means when he says
things about physics.

> As for the methodology of my poll, I simply stuck my head in each
> office and, without any context, announced that I was taking a
> poll:  "Is entropy objective or subjective?".  All but one answered
> "objective".  Then I e-mailed my former instructor, again with
> no context, and he answered "subjective" (with a nice brief
> explanation along the lines of what I've been arguing).  I only
> "badgered" one person, the one who changed his answer from objective
> to subjective (though with some reservations that he's still
> thinking about).

You are a victim of the delusion that polls decide matters of fact.
That is not the case, newspaper headlines notwithstanding.

> > Will someone else please chime in here? A voice of sanity?
>
> I also would like to hear from some others.  It's becoming clear
> that further exchanges between Leigh and myself are not likely to
> get us much further.

I dunno, I might get more creative with my insults.

> > Would you insert comments about the
> > subjective nature of entropy into such a course? I'll wager that
> > the texts cited here would not support your view.
>
> In my course I raised the issue very briefly, several weeks ago,
> and said it's controversial.  Then this morning, as students were
> coming in before class, I briefly mentioned this debate to them
> and asked if they had an opinion.  (Most of them did not.)  But I
> didn't spend any more class time on it.

You did them no great service. I do hope that at least those who
need to know learn that entropy is a function of the state of a
system. The topic of entropy was not controversial before this
discussion started.

> I've never seen a text that even raises this question, much less tries
> to answer it.  If you know of one that does, please tell me.  Landau
> and Lifshitz *almost* touch on the question, especially in their discussion
> of timescales on page 27 (statistical physics, part 1, 3rd edition).
> They say that there's no such thing as an "instantaneous" entropy,
> but rather that entropy is always understood to be relative to some
> relaxation timescale.  But I'm making a stronger claim, that even
> over very long timescales, most "accessible" states will never
> be realized and so the conventional entropy also factors in our
> large degree of ignorance (which could be somewhat less, yielding
> a smaller value of the entropy).

It seems to me that you are claiming that the entropy of a system is
a function that increases monotonically in time. Landau and Lifschitz
should probably discuss fluctuations in entropy (some texts do) in
connection with their statement about instantaneous entropy. When the
system has relaxed to the point where the rms fluctuations in the
entropy mask any deviation, the system is fully relaxed.

> Some other books define "accessible" in terms of "constraints".  But
> they're usually nebulous about what, exactly, qualifies as a constraint.

Well, volume is a constraint. So is internal energy. Given those
two one can calculate the entropy of a pure substance in equilibrium.
Let me anticipate your counterargument: if the energy is defined
precisely then it corresponds to exactly one eigenstate. Since it
seems that Nature abhors precise degeneracy this means there is only
one state which satisfies this constraint (not making the error of
exchanging identical molecules and calling the states different). Thus
S = k ln 1 = 0.

If the system is considered over a time interval delta t then its
energy uncertainty is delta E, and the order of the fuzzy degeneracy
soars to the skies. The ideal system I have set up as a straw man
has no physical instantiation. All physical systems are time limited.

Leigh