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From: desj@brahms.BERKELEY.EDU (David desJardins)
Newsgroups: net.physics,net.philosophy
Subject: Thermodynamics / Statistical Physics
Message-ID: <12662@ucbvax.BERKELEY.EDU>
Date: Tue, 25-Mar-86 18:39:42 EST
Article-I.D.: ucbvax.12662
Posted: Tue Mar 25 18:39:42 1986
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Reply-To: desj@brahms.UUCP (David desJardins)
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Xref: watmath net.physics:3974 net.philosophy:4679

Here is an interesting topic that came up in a private discussion.

I wrote:
>>Two definitions are equivalent iff they define the same set of things.

And Matt Wiener replied:
>Only in mathematics!
>
>Just because things turned out to be the same, didn't mean they HAD to be
>the same.  Is 'heat' the same as the thermodynamic definition of 'heat',
>(which I shall call td-heat) ?  If so, what *was* heat >200 years ago?  
>Is td-heat the best definition of heat or merely the most useful definition
>of heat?  In other words, does td-heat capture the *meaning* of heat or
>merely a physical law aspect of heat?
>
>My very ability to ask these questions, and to sense an underlying intent
>behind the question convinces me that td-heat is only an operational aspect
>of something wider.  But what that something is is beyond my ability to
>define.
>
>In other words, td-heat describes a particular relationship between a
>microscopic configuration and macroscopic state, whereas, heat is merely
>the macroscopic state, without the underpinnings.  To me, heat and td-heat
>describe the same things, not because they *mean* the same thing, but
>because physical law is what it is and not something else.

   Unfortunately (?) you have stumbled onto another of my favorite topics:
entropy and time-reversal.  The answer, which I feel very confident about
(as opposed to my philosophical ramblings) is that heat (like entropy) is a
*statistical* property.  And, in fact, heat is the statistical abstraction
of td-heat.

   To explain what that means, I am going to give you one of my standard
examples.  I am going to use very classical models of matter, although I
am pretty sure that more modern physics can be incorporated later if need be.
   Suppose we take a block of wood and let it slide down an inclined plane.
When it reaches the bottom its gravitational potential energy has been
converted to heat.  But at a microscopic level all that has happened is a
series of collisions/interactions between particles.  And in classical
physics all of these interactions are time-reversible.
   So now take that block and reverse the direction of motion of all of its
component particles!  We still have an equally random distribution of energy
(td-heat).  And also reverse the direction of motion of all of the components
in the inclined plane.  Again nothing deep, the same amount of td-heat.
   But now what happens?  The td-heat gets converted back into gravitational
potential energy as the block slides back up the plane!  All of the time-
reversible interactions that just took place are reversed!
   It looks like our td-heat wasn't really random enough!  It was just right
to make the object slide back up the plane!  But of course *every* possible
distribution of heat energy is going to behave this way in *some* (very
unlikely, of course) situation.
   Does this contradict the laws of thermodynamics?  Of course not, because
they are *statistical* laws.  When you talk about an object with a certain
heat, you are really talking about a "typical" object with that td-heat.
And, in general, you can also do the converse, in that an object with a
specific td-heat can *generally* be expected to behave as a typical object
with that heat.  But nevertheless each object individually *can* have its
own behavior; thermodynamics just talks about the statistical behavior of
them all as a class!

   All that thermodynamics is is *statistical physics*.  Take the laws of
physics, apply them to large collections of particles, and you find (!) that
these large collections behave in ways that can be understood without any
analysis of the motions of individual particles.  You only need to measure
a few statistical properties (like heat!) to predict the statistical behavior
of these systems.  Entropy lets you predict the probability of exceptional
event like the block sliding up the plane; the probability is exactly the
exponential of the difference in entropies!
   Now the fact is, that our universe *does* consist of large collections of
particles.  So we *do* in fact *see* this sort of statistical behavior.  We
can see that there is a fundamental property that we call heat, *even if*
we don't understand the fundamental nature of this property!

   As an interesting aside, if our universe were less complicated it would
be harder to understand!  If there were only 10^4 atoms/human the statistical
statements would not be nearly as strong!  And so the behavior of a chunk
of matter would be much *harder* to analyze, because you *would* have to
deal with the motions of the individual particles.

   -- David desJardins