Re: [Fis] Szilard's Engine and Information

Below I respond to Shu-Kun's most interesting posting.

>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.
     SS: Yes, we agree here. I like to add, however, that a highly
constrained system also has a very high potential H. That is, with many
constraints, many things can go wrong! A system must assume unusual
configurations in order to heal insults. That is, if a system is an
adaptable one, adaptability will involve taking up less frequent behaviors.
So, in a fluctuating eviroment, I think what we want to say is that with
increasing information bearing upon (or within) a system, the fewer are its
routine behaviors. That is, S actual = S maximum - I (See Brooks and
Wiley, "Evolution As Entropy").

>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
     SS: Yes. I note that this is quite close to Brillouin's negentropy
principle of information (NPI). That is, S actual = S max - I. So, I see
L as referring to S actual, or average routine behavior of the system.

(This is my unpublished work. Thermodynamics is a special case of
information theory criteria for conservation of certain structural
feature).
     SS: Yes. Formally we have: {Shannon concept { Boltzmann concept}}.

>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.
     SS: So, "sameness" relates to the disorder concept, which can be
applied anywhere.

>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.
     SS: That is to say, they interact in a thermal fashion.

>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.
     SS: I only qibble with your use of "spontaneous" here. I think the
separation of different substances requires energy input (which was applied
when O and W were stirred up to begin with).

>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.
     SS: So, here we have the thermal application of pressure replacing the
stirring.

>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".
     SS: This looks good to me.

>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.
     SS: And this supports my idea that the O/W separation is a thermal
one, NOT spontaneous.

>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.
     SS: Hmm. This seems a great simplification in undertsanding, if true.
I cannot comment because of my limited knowledge of muscle contraction.

>(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.)
     SS: So, it reprsents work.

>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 data 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.
     SS: Yes, this is the basis of my thinking about information.

>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.
     SS: OK. Energy gradients all represent information.

>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.
     SS: Yes. I will forward this posting to a biochemist who think
aboutthis kind of thing a lot.

>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.
     SS: No excuses necessary! It is always revealing to see a lot of
thought concisely presented.

STAN
>
>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 Mon Apr 19 14:07:10 2004