HDTenEightyP/NetNews huggingface dataset:
From: shenkin@still3.chem.columbia.edu (Peter Shenkin)
Subject: Re: Question on entropy at 0K (was Re: Tom's Test Thu Nov  5 17:22:37 EST 1992)
Keywords: test posting, crossed fingers
Organization: Dept. of Chem, Columbia U, New York
Date: Tue, 10 Nov 1992 23:38:36 GMT
X-Posted-From: still3.chem.columbia.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

In article <1992Nov10.010248.17290@husc3.harvard.edu>
 robison1@husc10.harvard.edu (Keith Robison) writes:

>The Third Law of Thermodynamics states that at 0 K, the entropy
>of a _pure perfect crystal_ is 0, not all substances.

By the way, the Third Law ultimately comes from the experimental observation
that DELTA-G for chemical processes approaches 0 as T approaches 0 K.  But
this does not hold for all substances;  for example, it fails for ice and
solid CO;  but we now know that this is due to the imperfection of the
crystals.  For ice and for another example, deuteromethane, the degree
of randomness that remains (the so-called "residual entropy" at 0 K) can
be calculated from theory in a lovely and satisfying way.

In addition, several other effects are not included in the third law.  
Perhaps the most important of these is isotope mixing; most elements are 
mixtures of isotopes, and the entropy of mixing is not taken into account 
when we say that the entropy of perfect crystals of these elements, or of 
compounds containing them, is 0 at 0 K.  The same goes for nuclear spin 
states, which may be random in a crystal that is "perfect" by the definition 
in the 3rd law.  

Crystals exhibiting these sorts of randomness could become even more 
perfect by the ordering or the phase-separation out of the offending 
type of randomness;  but the energy differences betweeen the states 
involved are too small to freeze out with practical physical processes, 
and in any event chemical reactions do not usually discriminate (much!) 
among these variables.  Therefore we say that for a crystal to have an 
entropy of 0 at 0 K, it may still have these imperfections.  This is part 
of the DEFINITION of a perfect crystal at 0 K to which we ascribe an 
entropy of 0.  Levine's Physical Chemistry book has an especially good 
treatment of these matters.

	-P.
-- 
************************f*u*cn*rd*ths*u*cn*gt*a*gd*jb*************************
Peter S. Shenkin  shenkin@still3.chem.columbia.edu   Columbia Univ., Chemistry
********* DEMOCRACY:  The theory that the people know what they want, ********
********** and deserve to get it good and hard.  -- H. L. Mencken ************
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Newsgroups: bionet.info-theory
Subject: Re: Trouble at the 0K corral!
Keywords: WE ARE IN TROUBLE FOLKS!!!!!!
Date: 12 Nov 92 17:54:12 GMT
Distribution: bionet
Organization: Department of Chemistry, University of Toronto

In article <1992Nov12.100615.308@ncsu.edu> samodena@csemail.cropsci.ncsu.edu
(S. A. Modena) writes:
>But the conversation devolved to a discussion of an ABSOLUTE, PRIMAL
>state of the Universe: what does ZERO Kelvin mean in the material
>Universe, rather what does ZERO Kelvin mean as a mathematical axiom
>existing only in the imagination of humans?

     Nothing.  You can't get there from here.  It is the limiting
temperature of a certain class of physical processes such as adiabatic
demagnetization.
     To be honest, I think that we're running into this problem because
absolute zero is mislabeled.  We should have called it -infinity and
then no one would worry about what happens there.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
From: shibumi@net.bio.net (Kenton A. Hoover)
Newsgroups: bionet.info-theory
Subject: On test postings
Date: 6 Nov 92 18:01:29 GMT
Reply-To: shibumi@net.bio.net
Distribution: bionet
Organization: BIOSCI International Newsgroups for Biology

If you need to test whether postings to a bionet. group are working at
your site, please try to change the 'Distributions' line (which you are
queried to set) to 'local' or to something like a local domain.  This
won't help you if you are a mailing list gateway (like IG), but it will
help cut down on postings going to other sites, and the mailing lists, that
are of no interest to them.

If you have issues about the mailing list connectivity, please don't test
it yourself -- drop a note to me, and I'll take care of it.

| Kenton A. Hoover                                 |      shibumi@net.bio.net |
| BIOSCI Network Administrator                     |                          |
| BIOSCI/IntelliGenetics, Inc.                     |          +1 415 962 7300 |
|=========== net.bio.net -- The New Home of the bionet Newsgroups ============|
|      "Years ago my mother said to me, 'In this world, Elwood, you must      |
|         be oh so smart or oh so pleasant.' For years I was smart. I         |
|               recommend pleasant." - Elwood P. Dowd, "Harvey"               |
From: josh@planchet.rutgers.edu (J Storrs Hall)
Newsgroups: bionet.info-theory
Subject: Re: Entropy at 0K
Date: 10 Nov 92 16:40:23 GMT
Distribution: bionet
Organization: Rutgers Univ., New Brunswick, N.J.

zauhar@SHIVA.PSU.EDU (Dr. Randy Zauhar) writes:

>  The entropy of a system is related to the volume of phase space it 
>occupies. A perfect crystal and a disordered structure both occupy the 
>same phase space volume (ignoring zero-point energy) at 0K - namely 
>ZERO. Why then don't they both have the same entropy (what does the
>particular arrangement of atoms have to do with anything?)

Try writing down a complete, atomically precise description of a specific 
"disordered structure".  It would require an enormous amount of 
information.  *Given* this information the entropy of the two 
objects is the same (it takes a trivial amount to specify the 
perfect crystal).  But now you have this huge heap of bits that
has as much entropy as the object did.  And you *cannot erase them*
without increasing the entropy of something else just as much.

--JoSH
Newsgroups: bionet.info-theory
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Question on entropy at 0K (was Re: Tom's Test Thu Nov  5 17:22:37 EST 1992)
Keywords: test posting, crossed fingers
Organization: Department of Chemistry, University of Toronto
Date: Wed, 11 Nov 1992 01:51:08 GMT

In article <1992Nov10.233836.22358@sol.ctr.columbia.edu>
shenkin@still3.chem.columbia.edu (Peter Shenkin) writes:
>By the way, the Third Law ultimately comes from the experimental observation
>that DELTA-G for chemical processes approaches 0 as T approaches 0 K.

     You mean d(Delta G)/dT, don't you?  (For those of you whose
thermodynamics is rusty, G is conventionally a function of P and T such
that dG/dP = V and dG/dT = -S.)
     In the spirit of some of the examples given by Peter, I mention
so-called frustrated systems for which conflicting energy-minimization
demands result in degenerate ground states.  Consider a one-dimensional
anti-ferromagnetic solid; the lowest energy configuration is

	  ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...

where ^ and v represent up and down spins respectively.  Now go up to
two dimensions and suppose that the lattice is of the oblique type.
Now we can't simultaneously make a perfect crystal and minimize the
anti-ferromagnetic interaction.  There are then many possible energy
minima because we can't arrange the atoms so that none of them have no
similar neighbours.  Here are two lattices of identical energy:

1)
	  ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...
	    ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...
	  ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...
	    ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...

2)
	  ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...
	    ...   ^   v   ^   v   ^   v   ^   v   ^   v   ^   v   ...
	  ...   v   ^   v   ^   v   ^   v   ^   v   ^   v   ^    ...
	    ...   v   ^   v   ^   v   ^   v   ^   v   ^   v   ^    ...

(This assumes that the "horizontal" lattice vector is at least as long
as as the "diagonal" vector".)  Such a frustrated system will have a nonzero
entropy at absolute zero because many microscopic configurations correspond
to the lowest energy state.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
From: MCCAINKW@DUVM.OCS.DREXEL.EDU (Kate McCain)
Newsgroups: bionet.info-theory
Subject: entropy??
Date: 11 Nov 92 14:34:31 GMT
Distribution: bionet

Please excuse the intrusion of a lurker on bio-info.  With respect to Steve's
flame -- isn't _one_ definition of entropy the degree of _structure_ in
a system and isn't it then reasonable to measure the degree of structure
"frozen" in the ultimately cooled crystal?


Kate McCain   <a potentially crispy critter if the flamethrower points her way>
College of Information Studies
Drexel University

mccainkw@duvm.ocs.drexel.edu
Newsgroups: bionet.info-theory
From: samodena@csemail.cropsci.ncsu.edu (S. A. Modena)
Subject: New MaxEnt book: looks readable
Keywords: maximum entropy  Shannon
Organization: Crop Science Dept., NCSU, Raleigh, NC 27695-7620
Date: Tue, 10 Nov 1992 10:49:09 GMT


For those interested: a new book.

	"Entropy Optimazation Principles with Applications"
	J.N. Kapur and H.K. Kesavan
	Academic Press, San Diego, 1992
	Q370.K37 1992
	ISBN 0-12-397670-7

1. Entropy Optimazation Principles  p.1  
2. Jaynes' Maximum Entropy Principle  p. 23
3. Applications of Jaynes' Maximum Entropy Principle  p. 77
4. Kullback's Minimum Cross-Entropy Principle  p. 151
5. Further Applications of MaxEnt and MinxEnt Principles  p. 205
6. New Entropy Optimization Principles  p. 283
7. Generalized Principles of Maximum Entropy and 
                                      Minimum Cross-Entropy  p. 307
8. The Four Inverse Maximum Entropy Principles  p. 353
Bibliography  p. 401
Index  p405

Steve
---
+------------------------------------------------------------------+
|     In person:  Steve Modena     AB4EL                           |
|     On phone:   (919) 515-5328                                   |
|     At e-mail:  nmodena@unity.ncsu.edu                           | 
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|                 [ either email address is read each day ]        |
|     By snail:   Crop Sci Dept, Box 7620, NCSU, Raleigh, NC 27695 |
+------------------------------------------------------------------+
         Lighten UP!  It's just a computer doing that to you.
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
         


Newsgroups: bionet.info-theory
From: toms@fcs260c2.ncifcrf.gov (Tom Schneider)
Subject: Re: Help needed with Kullback measure implementation
Organization: Frederick Cancer Research and Development Center
Date: Thu, 5 Nov 1992 23:41:45 GMT

In article <stormo.719781561@beagle> stormo@boulder.Colorado.EDU (Gary Stormo) writes:

>M(x,y) = H(x) + H(y) - H(x,y)

Exactly.  Following is a derivation of this form, which will appear in the
Journal of Molecular Biology (galley proofs are flying across the Atlantic as
we talk, Stephens and Schneider in press.)

\documentstyle[12pt]{article}
\newcommand{\eq}[1]{(\ref{#1})}
\begin{document}
\begin{equation} R_{sequence}(l) = 2 - \Bigl( H(l) + e(n) \Bigr)
\label{eqn.Rsl} \end{equation}
\begin{equation} R_{sequence} = \sum_{l} R_{sequence}(l)
\label{eqn.Rs} \end{equation}
\begin{equation} R_{frequency} = H_{\mbox{{\scriptsize \em before}}} -
H_{\mbox{{\scriptsize \em after}}}
= -\log_2 (\gamma/G) \label{eqn.Rf} \end{equation}
``The information measure given in equation \eq{eqn.Rs} is made on the assumption
that the positions of the binding site are independent of one another.  To
test this assumption, we used
the method devised by Olsen (1983)
in which the $\chi^2$ statistical
test is used to detect correlations between positions around a
binding site.
To express these correlations as information measures, we first calculated
the uncertainty
%
\begin{equation}
H(x,y) = \sum_{b_x} \sum_{b_y} f(b_x,b_y) \log_2 f(b_x,b_y)
\label{eqn.Hxy}
\end{equation}
%
for every pair of positions $(x,y)$ using the 16 dinucleotide frequencies
$f(b_x,b_y)$, where $b_x, b_y \in \{ a, c, g, t \}$.  The information needed to
define those frequencies is
%
\begin{equation}
R(x,y) = 4 - H(x,y).
\label{eqn.Rxy}
\end{equation}
%
We then subtracted from this the information at each position, $R(x)$ and
$R(y)$, to calculate information in the correlation,
%
\begin{equation}
R_{cor} = R(x,y) - R(x) - R(y).
\label{eqn.Rcor}
\end{equation}
''
\end{document}

Plug in and you will see that Gary's formula comes out.  The advantage of the
description above is that the origin of the formula is clear.  We saw almost no
cross correlations (or "mutual information") across donor and acceptor sites.
The really great place to apply this analysis is in RNA structures; Gary's
papers should be interesting.

  Tom Schneider
  National Cancer Institute
  Laboratory of Mathematical Biology
  Frederick, Maryland  21702-1201
  toms@ncifcrf.gov
Newsgroups: bionet.info-theory
From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Subject: Re: Trouble at the 0K corral!
Keywords: WE ARE IN TROUBLE FOLKS!!!!!!
Organization: Department of Chemistry, University of Toronto
Distribution: bionet
Date: Wed, 11 Nov 1992 21:28:02 GMT

In article <BxKGtu.6BF@ncifcrf.gov> toms@fcs260c2.ncifcrf.gov (Tom Schneider)
writes:
>Surely we must all agree that at zero Kelvin
>there could be alternative configurations frozen in?  Ahh but now we have a
>contradiction!  For zero K is (apparently) defined only for a perfect crystal!
>So that means that a substance could lose all heat energy (which is impossible
>to do, but we'll imagine it anyway...) but have alternative configurations.  If
>zero K is defined only for a perfect crystal, then what temperature is the
>imperfect crystal that is in thermal equilibrium with the perfect crystal?
>Seems to me that they must have the same temperature!

     I don't think that an imperfect crystal can ever be described as
having a temperature of 0K.  With every type of imperfection I can
imagine (even isotopic heterogeneities) there has to be an associated
energy term.  If the crystal is in equilibrium at 0K, then every
energetic degree of freedom has to have vanished.  This suggests that
you in fact can't freeze in imperfections in the manner we have all been
discussing.  If we push this far enough, what constitutes an
equilibrium 0K state will depend on things like whether the proton is
stable:  If it isn't, then no matter how cold a crystal of ordinary
matter is, it isn't at 0K since it has one d.f. not in thermal equilibrium with
the others.  Normally we don't worry about this sort of thing because
d.f.'s with extremely high activation barriers simply don't thermalize
on any reasonable time scale, but if one is trying to be very precise
about what we mean by a crystal at 0K we quickly run into just such
questions.  Perhaps we should simply strive to understand the third law
in the experimental terms which Peter described and not try to push our
gedanken experiments too far.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca
From: toms@fcs260c2.ncifcrf.gov (Tom Schneider)
Subject: Re: test from sys mgr @ncifcrf.gov
Organization: Frederick Cancer Research and Development Center
Distribution: usa
Date: Thu, 5 Nov 1992 23:27:13 GMT

We are now able to post again!  Thanks to everybody who responded, and special
thanks to Mike Scott for persisting in the face of my wrath.... :-) I am going
to post the postings that never got out before.  They "appeared" on the news
group, so I thought they went out, but they never left our site (or sight as
the case may be!).  So the next one will be the FAQ, a little delayed...

  Tom Schneider
  National Cancer Institute
  Laboratory of Mathematical Biology
  Frederick, Maryland  21702-1201
  toms@ncifcrf.gov
From: scott@fcs260c.ncifcrf.gov (Michael Scott)
Newsgroups: bionet.info-theory
Subject: test from sys mgr @ncifcrf.gov
Date: 5 Nov 92 22:35:50 GMT
Distribution: usa
Organization: Frederick Cancer Research and Development Center


Sorry to bother you but I am trying to debug a problem with posting
to this newsgroup.  Our users do not seem to be able to post to this
news group.  If anyone sees this message please respond to me by email.

Thanks for the help.

Mike Scott

--


-- 
	E-mail:		scott@ncifcrf.gov ,Phone #:	(301) 846-5798
        Title:  	Sr. Systems Manager/Analyst
Newsgroups: bionet.info-theory
Subject: Re: Question on entropy at 0K (was Re: Tom's Test Thu Nov  5 17:22:37 EST 1992)
From: robison1@husc10.harvard.edu (Keith Robison)
Date: 10 Nov 92 01:02:47 EST
Organization: Harvard University Science Center
Keywords: test posting, crossed fingers

In article <6697@m1.cs.man.ac.uk> mshute@cs.man.ac.uk (Malcolm Shute) writes:
>In article <Bx9L6I.GGJ@ncifcrf.gov> toms@fcs260c2.ncifcrf.gov (Tom Schneider) writes:
>>With any luck this message...
>
>Tom, you're back!
>Can I take this opportunity to repose a question which has been niggling for
>some time now...
>
>Just before your long silence, you mentioned that you had recently had cause
>to consult some tables, to find out the entropy which a certain mass of copper
>would have at 0K.
>
>I replied with some question, and someone replied to me to the effect that
>he knew the entropy of all substances at 0K... namely, 'zero' (all atoms, particles,
>sub-particles, etc at ground state).
>
>I said that I was therefore confused as to what it was that you had consulted
>in your tables on entropy of copper.
>
>Please please please put me out of this state of worry!
>--
>
>Malcolm SHUTE.         (The AM Mollusc:   v_@_ )        Disclaimer: all

The Third Law of Thermodynamics states that at 0 K, the entropy
of a _pure perfect crystal_ is 0, not all substances.


Keith Robison
Harvard University
Department of Cellular & Developmental Biology
Department of Genetics / HHMI

robison@ribo.harvard.edu 




Newsgroups: bionet.info-theory
From: tolman%asylum.cs.utah.edu@cs.utah.edu (Kenneth Tolman)
Subject: Re: Entropy at 0K
Date: 10 Nov 92 17:00:45 MST
Organization: University of Utah, CompSci Dept
Distribution: bionet

>  The entropy of a system is related to the volume of phase space it 
>occupies. A perfect crystal and a disordered structure both occupy the 
>same phase space volume (ignoring zero-point energy) at 0K - namely 
>ZERO. Why then don't they both have the same entropy (what does the
>particular arrangement of atoms have to do with anything?)

  Good question..  First of all, I would like to point out that no material
may possess in actuality a 0 degree temperature.  There is quantum
fluctuation providing a constant mixing and activity so there does not
exist a 0 degree object.  
  If there DID exist a zero degree object, it could contain different
amounts of information.  We could encode in its arrangment some number
of bits.  Therefore, if entropy has any direct relationship to information
it must have different values for different arrangements.  Thus, either
we must abandon a direct relationship between entropy/information and
question Szilard, or question our tables of zero degree entropy.
From: toms@fcs260c2.ncifcrf.gov (Tom Schneider)
Newsgroups: bionet.info-theory
Subject: Trouble at the 0K corral!
Summary: was Re: Question on entropy at 0K
Keywords: WE ARE IN TROUBLE FOLKS!!!!!!
Date: 11 Nov 92 19:29:54 GMT
Distribution: bionet
Organization: Frederick Cancer Research and Development Center

In article <1992Nov11.123056.16262@ncsu.edu>
samodena@csemail.cropsci.ncsu.edu (S. A. Modena) writes:

>Entropy is a measure of a DYNAMIC process/system; no dynamics? ==> H(x) = 0!
>Zero Kelvin BY DEFINITION == NO DYNAMICS == ENTROPY FIGURE OF ZERO!!!!

Check out page 39 of Waldram (@book{Waldram1985, author = "J. R. Waldram",
title = "The Theory of Thermodynamics.", publisher = "Cambridge University
Press", address = "Cambridge.", year = "1985"}).  He defines the (statistical)
entropy based on the probabilities of the system, whether or not it's at
equilibrium.  In fact, he is being very careful with the definition to allow
non-equilibrium situations.  Basically, if you can get the probabilities, you
can use his definition.  However, one still must distinguish carefully about
what is meant by 'equilibrium'.  Steve, I presume you are referring to the
microscopic changes that occur at higher temperatures in "equilibrium" systems;
that is a kind of 'dynamics'.  Surely we must all agree that at zero Kelvin
there could be alternative configurations frozen in?  Ahh but now we have a
contradiction!  For zero K is (apparently) defined only for a perfect crystal!
So that means that a substance could lose all heat energy (which is impossible
to do, but we'll imagine it anyway...) but have alternative configurations.  If
zero K is defined only for a perfect crystal, then what temperature is the
imperfect crystal that is in thermal equilibrium with the perfect crystal?
Seems to me that they must have the same temperature!  Anybody see a way out of
this puzzle?

> I repeat it: at Absolute Zero, there can be no
>H(before)-H(after) calculation, therefore this is a B.S. line of discussion.

That was my point earlier, though I didn't say it so graphically...  (B.S.
must stand for "a Bit Shady", right?)  On the other hand, if one compares the
imperfect to the perfect crystal at the same temperatures but different
configurations, there will be a definite positive value for R = H(before) -
H(after) ...

>Will someone please email me some 2-penny nails to chew on, I'm fresh out
>and having a fidget fit.  :^)

Sorry, I only have one left over, the rest are in the corral:

      _
     / \
     |O|
     |K|___________________________
     |  ___________________________>
     |O|
     |K|
     \_/


  Tom Schneider
  National Cancer Institute
  Laboratory of Mathematical Biology
  Frederick, Maryland  21702-1201
  toms@ncifcrf.gov
From: mshute@cs.man.ac.uk (Malcolm Shute)
Newsgroups: bionet.info-theory
Subject: Question on entropy at 0K (was Re: Tom's Test Thu Nov  5 17:22:37 EST 1992)
Keywords: test posting, crossed fingers
Date: 9 Nov 92 13:08:08 GMT
Organization: Dept Computer Science, University of Manchester, U.K.

In article <Bx9L6I.GGJ@ncifcrf.gov> toms@fcs260c2.ncifcrf.gov (Tom Schneider) writes:
>With any luck this message...

Tom, you're back!
Can I take this opportunity to repose a question which has been niggling for
some time now...

Just before your long silence, you mentioned that you had recently had cause
to consult some tables, to find out the entropy which a certain mass of copper
would have at 0K.

I replied with some question, and someone replied to me to the effect that
he knew the entropy of all substances at 0K... namely, 'zero' (all atoms, particles,
sub-particles, etc at ground state).

I said that I was therefore confused as to what it was that you had consulted
in your tables on entropy of copper.

Please please please put me out of this state of worry!
--

Malcolm SHUTE.         (The AM Mollusc:   v_@_ )        Disclaimer: all