From: mroussel@alchemy.chem.utoronto.ca (Marc Roussel)
Newsgroups: bionet.info-theory
Subject: Re: A Mathematical Fireside Chat at 300K about 0K
Date: 15 Nov 92 16:34:36 GMT
Distribution: bionet
Organization: Department of Chemistry, University of Toronto

In article <1992Nov14.234006.12491@news2.cis.umn.edu> burchard@geom.umn.edu
(Paul Burchard) writes:
>In article <1992Nov14.160532.13636@alchemy.chem.utoronto.ca>  
>mroussel@alchemy.chem.utoronto.ca (Marc Roussel) writes:
>> In article <1992Nov14.080455.6956@news2.cis.umn.edu>
>> burchard@horizon.math.utah.edu (Paul Burchard) writes:
>> >Thermodynamics may be understood as the study of energy and the way it
>> >is distributed among the parts of a system.  The fundamental assumption
>> >that the subject makes about energy is that it is a *positive* quantity.
>> 
>>      That's wrong.  We have no way of assigning a zero point to energy
>> and we only measure differences.  All zero points for energy are purely
>> conventional and recognized as so by all physicists I know.
>
>I am not wrong.  First of all, at this point I am only claiming that 
>thermodynamics *wants* positive energy.  This is necessary because otherwise 
>there is no concept of a "heat bath" which is characterized purely by its 
>temperature---unless you impose the positivity constraint, there will be
>no well-defined maximum entropy distribution.

     Thermodynamics gets on quite well without a positive energy scale.
Temperature in thermodynamics is defined as that variable of state which
characterizes thermal equilibrium.  A heat bath is large body of
constant temperature, i.e. one which is in internal thermal equilibrium.
Thermal equilibrium means that no heat flows in the absence of an
adiabatic wall and heat is a form of energy which flows without
macroscopic work being done either on or by the system.  I never had to
involve ANY energy scale in this definition.  If you want to stand
physics on its head, you're going to have to tell us what's wrong with
this, our normal way of thinking of temperature.
     Rather than thermodynamics, I think you want to discuss statistical
mechanics.  (They are not entirely the same thing, although modern usage
sadly confuses the two more and more.)  If you look at how we write down
partition functions and derive other quantities from them, you find that
differences in state functions are independent of the choice of zero
point energy.  I don't give a hoot about anything else because I can't
measure absolute values of energy or entropy.

>Second, many quantum field theories do provide a natural zero energy
>reference point, such that a difference between this reference level and
>the ground state has physical consequences.

     I will grant you that.  However, I don't know of a q.f.t. that
predicts thermodynamic consequences of this zero reference point.  If
you do, let me know.

>> >In this way we find that our best guess is the exponential distribution
>> >p(E) = (1/T) e^{-E/T}.
[...]
>That's just the *most generic* distribution having
>a specific temperature; therefore it should be the distribution in the case
>of a heat bath which we assume to have no further properties.

     This is backwards from the way we do physics.  It doesn't tell me
how to measure temperature, therefore it is physically meaningless.  It
is senseless to pretend that we don't know what temperature is.
Temperature is a primitive concept which we get from thermodynamics.
The job of statistical mechanics is to connect this primitive to
microscopic mechanics, not to invent temperature de novo.

>The entropy of any continuous probability distribution is infinitely larger
>than that of a discrete one.  I challenge you to make sense of the limiting
>entropy of a sequence of continuous distributions, when the entropy measured
>from the continuous point of view is approaching minus infinity.

     I am going to be honest and admit that I have no idea what you're
talking about here.  I honestly don't see the pathology you describe in
the theory.  Maybe if you rephrased this in terms of partition functions
I would get it.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca