Re: [Fis] Szilard's Engine and Information

Dear Stan,

1. Thanks for considering "order" and "constraint".

Let us forget symmetry first: "more constraints, more order" should be
accepted.

To be complete, a system has higher "order" may imply
the following: if there are more constraints, there will be less
freedom, less dynamic,
more static and more confined; (or less symmetric), more information,
less entropy
and higher "order". (I guess this is what you meant by "constraints" in
another
thread where you said "further constraints are bearing upon some
systems, hemming them
in with a greater burden of information". Constraints made a structure
with a higher
amount of information.

Keep this in mind, let us examine two examples: 1. the constraint is the
wall
separating two ideal gases (oxygen and nitrogen). 2. the constraint is the
wall separating oil and water.

Excuse me but let me try to sell my humble theory called "similarity
principle" here.
It says that entropy increases with the increase in the property
similarity of the
components (see my S-Z plot at http://www.mdpi.org/lin/). This is the
basis of
my revision of the information theory where information and entropy are
defined
and their general properties are expressed as three laws similar to
thermodynamic
laws. For example, Energy (E) divided by (kT, k is Boltzmann constant, T
is temperature) will
give a dimensionless measure called L. The first law of thermodynamics
E=kTS+F
(F is free energy) will become L=S+I (This is my unpublished work.
Thermodynamics is a special case of information theory criteria for
conservation
of certain structural feature). During a process, the increased similarity
among two parts of a system will increase entropy and reduce information.

1.1. The two parts of ideal gases may have other difference in (P),
temperature (T) or chemical
concentration or in density, and will be a spontaneous process if the
constraint
is removed. At the end, the two ideal gas parts become the same (in P, T and
density, etc.): the system seeks such sameness, driving by information loss
(in thermodynamics, potential or free energy reduction) or entropy increase.

They (oxygen and nitrogen) would like to aggregate because they are both
the same kind of substances: both are ideal gas. However, a constraint
can maintain
other differences (P, T, etc., or one side has concentration of oxygen
100% and nitrogen 0%,
the other side has oxygen 0% and nitrogen 100%) and order.

1.2. Unlike ideal gases (nitrogen and oxygen) which are intrinsically
the same
to a device measuring P and T (or kinetic energy of the molecule),
oil and water are regarded as intrinsically different. A constraint is
not required
to separate the two phases. Therefore, the arrangement of oil and water
droplets may be used to record data in a solid device.

Truly different substances spontaneously separate because the same
substances
O and O would like to aggregate and W and W would like to aggregate. As
a result,
O and W are separated. This follows my similarity principle pretty well.
Now the constraints are needed to stop O and O droplets from aggregation
to maintain the information.

The property similarity can be controlled by certain operation (I
remember a colleague
just discussed the word "operation" in another thread): pressure (P) and
temperature (T) control.
At certain very high P and very high T, water (W) and oil (O) will
spontaneously
mix to form a homogeneous fluid phase. Then, only constraint (a wall) can
separate them and can maintain the "order" or the orderly structure and
maintain
the final 2 bits of information.

The gravity of the Earth will further reduce the similarity between
water and oil and
will facilitate their separation at low temperature. I got my Ph.D. from an
organic chemistry laboratory and I was a postdoc doing organic
chemical synthesis (preparing all kinds of "oil", the so-called organic
compounds)
in a medicinal chemistry labor where the W/O separation in a separation
funnel,
the so-called hydrophobic effect, was used daily. I also add salts to
the water
phase to make the aqueous phase more aqueous and more different from
the oil phase. I find everything I observed fits into my "similarity
principle".

2. Szilard's Engine and Information

Mixing of different ideal gases (oxygen and nitrogen) originally
separated in
two parts of a rigid container at the same and unchanged T and P cannot
generate
any mechanical work. This is for sure. If Szilard's Engine works, the
2nd law will be no law at all. Of course Szilard's discussion
contributed tremendously to information theory.

However, if the constraints separating an ideal gas into
two or more parts in flexible containers (gas bubbles in a liquid phase),
the aggregation to form a bulky gaseous phase can generate mechanical work
if there is a suitable machine. This is similar to oil droplets
aggregation in water
to form a bulky oil phase. Oil/water separation at a lower temperature can
create mechanical work. This might be the very mechanism of
our muscle contraction and relaxation cycle to do animal work. The machine
(an Engine) is an animal muscle cell. Gas bubbles in water and oil
droplets in water have the same
kind of constraints and obeys the same kind of "order", in my humble
opinion.

(Ideal gas molecules by definition do not have molecular interaction.
Here we ignore molecular interaction among molecules in a bulk condensed
phase
and on the interfaces. Hydrophobic effect has been explained mainly by
surface free energy consideration.)

3. Information (I) is the measure of the compressed data

Finally, as a chemist, my interest is to use information (I) to
characterize the
structures and their stability of a molecular system. I am sure different
structures with different constraints (either macroscopic or microscopic
constraints) represent different amount of information. The difference
and the information change can be experimentally (operationally)
measured by monitoring certain chemical and physical properties before
and after
the constraints are removed. To make any progress on this direction,
it is necessary to define information (I). My definition of information (I)
is the measure of the compressed data. If the amount of date cannot be
compressed
any further, that amount is called information (I). Then, the maximum
data is L.
Entropy S=L-I. Lewis, Brillouin and many other people accepted "information
loss = entropy increase" relation. Shannon's consideration is a dynamic
channel of communication. Shannon basically call entropy something like
"entropy
of information " (or entropy of signal, entropy of a set of symbol,
etc.). Loet's
comments are correct for other area of studies where we may tolerate if the
difference between entropy and information concepts are not told.
However, because we are doing science, it is always very important (at least
harmless) to define clearly the obvious. If information (I) is defined,
we can work.
My interest as a chemist is a static structure (not a communication channel)
and there is always an information amount. Even for an ideal gas where
molecules are always in kinetic motion, if it is confined in a chamber,
the chamber (a constraint) defines a static structure for the ideal gas.
Electrons and nuclei are confined in a static structure called molecule.
Therefore we can consider individual molecule and its stability by
information theory.

Excuse me also for my repeated presentation because I think I expressed
these ideas many times before, at least when we were discussing
molecular recognition.

Best regards,
Shu-Kun

Stanley N. Salthe wrote:

>Shu-Kun said:
>
>
>>Regarding the related entropy of mixing (Delta S), it is certain that >the
>>entropy of mixing is an information theoretical entropy >because there is
>>no heat involved. It should not be taken as a typical >thermodynamic
>>entropy (Delta S). Mixing of two chiral molecules >gas R and gas L you
>>mentioned cannot be a thermal process. Therefore, >it is not a
>>thermodynamic process in an heat engine. Mixing of R >and L cannot be used
>>to generate mechanical work. This is a fact. >When we discuss the engine
>>and related possibility of energy >conservation, this fact must be kept in
>>mind. > >If the mixing of gas R and gas L would create work (a kind of
>>mechanical >energy calculated as distance times force), one should be able
>>to also create >mechanical work by mixing red color and black color.
>>
>>
>
>to which I replied:
> SS: I find this interesting in regard to the understanding of
>physical entropy as disorder. This interpretation has been disputed because
>of examples like mixtures of oil and water, which seem to spontaneously
>separate, making a more orderly result than was present in the mixed state.
>But Shu-Kun's posting here suggests why this understanding is specious.
>What is neglected in this view is that energy-utilizing work had to be done
>to mix the oil and water to begin with, in a thermal process. This process
>set up a curious kind of dispersed energy gradient, which then dissipated,
>producing the separation, and giving off heat again. That is to say, the
>unmixing of oil and water is a kind of work (not unlike the unwinding of
>many wound up rubber bands!), and, as such, would not be expected to
>produce disorder. Put another way, the unmixing of oil and water is NOT
>SPONTANEOUS, but is instead a massive amount of microscopic work.
>
>then Victoras said:
>
>
>> How would behave a mixture of oil and water if Earth's field of
>>gravitation was absent - would it mix or separate ? Can this be described
>>by a conditional sentence like the one below ? if (gravity
>>present){separation} else {mixing} Then it seems like an algorithmic
>>process where entropy produces opposite results given different initial
>>conditions. Thousands, millions, mirriads of similar conditional branches
>>take place every moment everywhere in the Universe. Thence everything can
>>be described/modelled as causal chains of events. That's how our
>>(natural) and artificial inteligence (rule based or case
>>(experience) based reasoning) work. Just interesting parralels...
>>
>>
>
>to which Shu-Kun replied: They would separate.
>
> SS: So, Victoras sees the energy gradient being used to power the work
>of separating oil and water as being gravitational energy, while Shu-Kun
>implies that it is instead some kind of chemical gradient. Either way my
>point is not being disputed. Therefore, even though the energy gradient
>dissipation view of entropy production is historically prior, and
>empirically measurable, the increasing disorder view is not falsified by
>this oil/water example in the way that some folks thought it was.
>
>STAN
>
>

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Received on Sat Apr 17 18:48:34 2004