I've received a lot of comments since posting my page on entropy and
evolution, but what has appeared here in response to my friday posting
has been by far the best technical comments I've received. I won't try to
respond to all the comments that have been made, I need some time to mull
them over anyways. I plan to revise the page soon, and some of the things
said here will certainly influence how I do.
One question that I have is where to find references to amorphous
materials having non-zero entropy at 0 K. Please understand that I don't
claim to be a thermodynamics expert, but rather someone who taught
thermodynamics and statistical mechanics for a couple of years at Acadia
University. (There is a difference.) My understanding has always been
much like what is given as one of the fundamental thermodynamic postulates
in Callen's "Thermodynamics and an Introduction to Thermostatistics"
(second edition), p. 30:
Postulate IV - The entropy of any system vanishes in the state for which
(dU)
(--) = 0 (that is the zero of temperature)
(dS)V,N1,N2...Nr
and that this can be understood statistically by the fact that at 0 K
there is only one state accessible to the system, regardless of whether
that system has structural disorder or not. If I am wrong about this, I
should like to have references to study the issue and find out where I
went wrong.
As far as the semantics go, I overstated things by calling this a pet
peeve. Rather I find that by equating disorder and entropy in a simple
fashion, one provides a little insight into entropy, and opens up a
multitude of possible misunderstandings. The latter are because
order/disorder are not well defined technical terms, but rather general
concepts. So for example, a person might say that evolution corresponds
to more order. Walking erect is more orderly than walking on all fours.
So evolution corresponds to decreasing entropy. Now we can and should
talk about open/closed systems etc here, but even before that I would say
that the simple understanding of entropy=disorder has led the person off
track.
In a given context we can offer a technical definition of disorder, in
relation to whatever defines the order of the system. So in a-Si research
we might take the bond lengths, bond angles, radial distribution function
etc of c-Si, and use the degree of fluctuation from these as a measure of
the disorder of the system. Each of these would give a different
number for the disorder of a given piece of a-Si. Multiple definitions
are possible, so in a technical context one must be clear about what is
meant by disorder in a system. Hence the futility of defining
entropy=disorder. It does aid a certain conceptual understanding, but I
am skeptical of what lies beyond that. The main dangers are either in
taking casual concepts of disorder and considering them to be a definition
of entropy (as the evolution example), or taking entropy as a general
definition of disorder (even though it cannot for example distinguish
between an ordered and shuffled deck of cards).
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| Doug Craigen |
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| If you think Physics is no laughing matter, think again .... |
| http://cyberspc.mb.ca/~dcc/phys/humor.html |
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