[Fis] Szilard's Engine and Information

Dear Colleagues,
I�ve attached a PDF version of this message for those whose browser
doesn�t do a good job of reproducing text formatting.
I am becoming more and more aware of the interest and help provided by
other academic disciplines toward my understanding of information and
entropy, and I appreciate Michel�s introduction in that regard. May I
suggest a powerful model from physics for understanding the
information-entropy relationship, at least as we physicists often use
those terms in thermodynamics and measurement? ( I was an experimental
particle physicist once, at the Los Alamos meson factory, then, in
Switzerland working for the ETH on elementary particle experiments. I�ve
taught at various universities in the U.S., and am now semi-retired.
But, I�ve retained an abiding interest in quantum measurement, which has
led to analysis of the Szilard engine and to calculation of the entropy
cost of information processing. I expect I may return to full time work
in some field related to quantum measurement or quantum information, if
such an opportunity arrives. So, my experience and perspective is
largely as a practicing physicist.) I understand that this model won�t
address many of those concepts enumerated by Michel.
By far, the most effective and powerful physics model I know for
investigating the relationship between thermodynamic entropy and
information is the Szilard engine (Szilard, Z. Physik, 53, 1929, p. 840;
Devereux, Found. Phys. Lett. 16, 1, 2003, p. 41, also available on the
web from the Entropy server). Szilard discovered a very simple model
that serves both as a heat engine and an information engine. It bridges
the gap between a macroscopic measuring apparatus and microscopic
information bit. Can anyone suggest a better model from physics? I�ve
found it extremely useful for understanding the cost, in terms of energy
and entropy, of quantum measurement, as well as the thermodynamic
entropy needed for information processing. Specifically, the
�information� here is the location, from measurement, of a single gas
molecule in one or another half of a macroscopic cylinder.
But, the fatal problem with use of the Szilard engine model had been
mistaken analysis of the engine cycle. Szilard suggested that the
apparatus for measuring location of the gas molecule within the engine
cylinder must produce entropy at measurement, in order to protect the
Second Law of Thermodynamics. For nearly seventy-five years now,
scientists have elaborated, expanded, and formalized that idea. (Zurek
in Frontiers of Nonequillibrium Statistical Physics, 1984, p. 151;
Lubkin, Int. J. Theo. Phys. 26, 1987, pp. 523-535; Brillouin, J. App.
Phys., 22, 3, 1951, p. 334; etc. )
But, Szilard�s suggestion is mistaken, and quite obviously so, with a
little careful consideration. In his model, after measurement of the
location, either R or L, of the molecule in one side or the other of
each of N cylinders of this engine, the memory register of the
measurement apparatus will indicate, for example, (R, L, R, R, L,
R,.....). That information is now fixed; it does not change over time
with fluctuations of the thermodynamic system, as the engine�s gas
molecule continues to collide with the cylinder. So, the
information-dependent entropy of the apparatus is zero. Analogous, for
example, to an ideal gas with the position and momentum of each gas
molecule fixed at specific values. That entropy is zero. (As physicists
calculate such things.)
Thus, the apparatus entropy could not have increased with measurement,
and the Second Law is not protected from Maxwell�s demon by an apparatus
entropy increase. Two philosophers of science, Earman and Norton, (Stud.
Hist. Phil. Mod. Phys., Vol. 30, No. 1, pp. 1-40, 1999) published a
quite extensive review of attempts to defend the Second Law from
Maxwell�s demon with information-generated entropy, and found no
creditable affirmative arguments. (Zurek, in the article cited above,
wrote that the measurement outcome is unknown to some external observer,
and so, the apparatus entropy is seen to increase by that observer. But,
the demon observer must know the measurement outcome for every cylinder,
in order to run the engine, and so he finds zero apparatus entropy. As
we all know, no scientific law, including the Second Law, is observer
dependent. If the demon observes no increase in entropy, then all
external observers must also find no increase. This was one of my
arguments against Zurek�s analysis. Earman and Norton offered another. I
think Zurek�s idea is similar to von Neumann�s notion that quantum
measurements are only completed when they become conscious to a human
observer.)
I calculated the entropy change of the Szilard measurement apparatus
(cited above). That entropy actually DECREASES by Nk ln(2) at
measurement, indicating an apparatus (thermodynamic) information
increase. Recall, however, from Maxwell�s original idea, that the demon
operating such an engine not only measures the properties of the gas
molecules, he also must move the cylinder partition. The Second Law
would not be violated if such partition activation produced sufficient
entropy. I believe this effect may be general for the usual type of
Maxwell demons: that it is partition movement (door closure, etc.) which
generates the entropy prescribed by the Second Law, not the entropy
which is associated with the information of measurement. In spite of the
innumerable publications claiming otherwise.
I�m somewhere near the middle of the calculation of the entropy
generated by partition movement in Szilard�s engine. I think I can make
that calculation quite general, and it appears, then, that I can use
that result to determine the fundamental entropy cost of information
processing. I mean what I�ve understood Charles Bennett and Rolf
Landauer to mean by such things: entropy in terms of, say, the Gibbs
formulation, and information processing as the logical manipulation of
an information bit (erasure, overwriting, etc.). (The renowned
philosopher of science, Karl Popper, thought that the Szilard engine
could be operated without measurement, and thus, with no information
transfer. If so, the engine might teach nothing about the relationship
of entropy to information. But, Zurek displayed the quantum mechanical
calculation for closure of the partition. The engine gas is not confined
to half the cylinder by partition closure alone, but rather by the
quantum measurement which follows closure. So, there must be information
transfer to run the engine.) And, recall that the Szilard engine has
been used by Charles Bennett and others as the model for information
stored in a memory register. And, removal of the engine partition,
followed by the measurement which reduces the quantum wave function,
erases the information originally stored in the (engine) register
(R,L,R,R,L,R,L,....).
Calculation of the entropy produced by partition closure isn�t quite as
simple as I once assumed, though the results now seem to give the value
I had anticipated. I do think it�s clear, in general, that prompt
movement of a physical object, like the engine partition, will produce
thermodynamic entropy. Consider the movement of the cylinder in a heat
engine, for example. (No quasi-static processes allowed.)
The calculation, so far, is incomplete, but it has shown something I
find really remarkable. The specific information needed to run the
Szilard heat engine is carried by a time signal, not by change in a
macroscopic physical configuration of any type. It�s this time signal
which causes the decrease in apparatus entropy, since it specifies the
captured molecule�s position. No heat is transferred to or from the
apparatus at measurement, so it shows no change in Clausius� entropy,
Delta Q / T. I�m unaware of any definition of entropy which explicitly
includes a time dependence. Does anyone else know of such?
I think there is, however, a change in entropy, (and, of thermodynamic
information) as determined by the Shannon-von Neumann probability
formulation. I suspect that, in determining the probabilities we assign
to thermodynamic configurations, we must include those that are
time-dependent. And, I�ve found that the entropy cost of partition
movement also depends on the time employed for that movement.
Thank you, Michel, for the introduction and direction for this discussion.

Cordially,

Michael Devereux

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