Fwd: Edwin T. Jaynes: Information Theory and Statistical Mechanics
Evgenii Rudnyi
could be of interest here as well.
Evgenii
-------- Original Message --------
Subject: [bC] Edwin T. Jaynes: Information Theory and Statistical Mechanics
Date: Fri, 12 Mar 2010 22:22:30 +0100
From: Evgenii Rudnyi <use...@rudnyi.ru>
Reply-To: biot...@lists.ccon.org
To: biot...@lists.ccon.org
I would like to thank Terren and Larry who brought my attention to works
of Edwin T. Jaynes. Both papers are available in Internet (the links are
in Wikipedia)
http://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes
and I have browsed them to look at the logic behind the statement about
the equivalence between thermodynamics and information entropies. Below
there are some my comments.
In the papers, the author considers statistical mechanics only, so let
me first describe the relationship between classical and statistical
thermodynamics. As the name says it, classical thermodynamics was
created first. It was not an easy born (see for example, Truesdell’s The
Tragicomical History of Thermodynamics) and many people find classical
thermodynamics difficult to understand. No doubt, the Second Law here is
the reason; people find it at least as non intuitive. On the other hand,
statistical thermodynamics was based on the atomic theory and here was
the hope to find a good and intuitive way to introduce entropy. Well, it
actually did not happen.
In order to explain you this, let us consider a simple experiment. We
bring a glass of hot water in the room and leave it there. In some time
the temperature of the water will be equal to the ambient temperature.
In classical thermodynamics, this process is considered as irreversible,
that is, the Second Law forbids that the temperature in the glass will
be hot again spontaneously. Actually it is in complete agreement with
our experience, so one would expect the same from statistical mechanics.
However there the entropy has some statistical meaning and there is a
nonzero chance that the water will be hot again. Moreover, there is a
theorem (Poincaré recurrence) that states that actually if we wait long
enough then the temperature of the glass must be hot again. No doubt,
the chances are very small and time to wait is very long, in a way this
is negligible. Some people are happy with such statistical explanation,
some not.
Therefore the goal of both papers is to bring a new vital force to
statistical mechanics. The author uses the formal equivalence between
the Shannon’s and thermodynamic entropies and based on this suggests
entropy inference or subjective statistical thermodynamics. I should say
that I really enjoyed the first paper. Here the assumption is that as we
do not have complete information about the system, we use what is
available and then just maximize the entropy to get the most plausible
description. In a way it is some data fitting problem and it seems to be
similar to the maximum likelihood in statistics. Yet, the term
information here is more like available experimental data about the system.
Unfortunately I was not able to follow the logic in the second paper. It
could be that I am already tired, it could that here the author
considers quantum statistical mechanics (quantum mechanics as such
brings new paradoxes). So I will make just a couple of citations that I
do not understand.
"With such an interpretation the expression "irreversible process"
represents a semantic confusion; it is not the physical process that is
irreversible, but rather our ability to follow it. The second law of
thermodynamics then becomes merely the statement that although our
information as to the state of a system may be lost in a variety of
ways, the only way in which it can be gained is by carrying out further
measurements."
"It is important to realize that the tendency of entropy to increase is
not a consequence of the laws of physics as such, … . An entropy
increase may occur unavoidably, due to our incomplete knowledge of the
forces acting on a system, or it may be entirely voluntary act on our part."
Could someone tell me what does it mean in respect to the experiment
with a glass of hot water? I would really appreciate it.
Best wishes,
Evgenii
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