Re: [Fis] FIS / introductory text / 5 April 2004

">" should be "=". I mean Delta "S = - Delta (information)". Sorry.

Dr. Shu-Kun Lin wrote:

> Dear Loet,
>
> You mean entropy S is equal to information (I), or almost equal. Can
> you still give
> a little bit of sympathy to the relation that Delta S > - Delta
> (information) and make some
> comments on this different relation? If we can agree on the relation that
> Delta S > - Delta (information),
> then we are ready to ask
> "why information loss is related to entropy", a question asked by
> physicists at the
> http://www.lns.cornell.edu/spr/2000-12/msg0030047.html website,
> and try to answer.
>
> Michel, thank you for your introduction.
>
> Shu-Kun
>
>
> Loet Leydesdorff wrote:
>
>> Dear Michel,
>>
>> The relation between thermodynamic entropy and the information is
>> provided by the Szilard-Brillouin relation as follows:
>>
>> Delta S >= k(B) Delta H
>>
>> (W. Ebeling. Chaos, Ordnung und Information. Frankfurt a.M.: Harri
>> Deutsch Thun, 1991, at p. 60.)
>>
>> k(B) in this formula is the Boltzmann constant. Thus, a physical change
>> of the system can provide an information, but it does not have to.
>> Unlike the thermodynamic entropy, probabilistic entropy has no
>> dimensionality (because it is mathematically defined). The Boltmann
>> constant takes care of the correction in the dimensionality in the
>> equation.
>>
>> When applied as a statistics to other systems (e.g., biological ones)
>> one obtains another (specific) theory of communication in which one can
>> perhaps find another relation between the (in this case biological)
>> information and the probabilistic entropy. This can be elaborated for
>> each specific domain.
>>
>> With kind regards,
>>
>>
>> Loet
>>
>>
>>
>> _____
>> Loet Leydesdorff
>> Science & Technology Dynamics, University of Amsterdam
>> Amsterdam School of Communications Research (ASCoR)
>> Kloveniersburgwal 48, 1012 CX Amsterdam
>> Tel.: +31-20-525 6598; fax: +31-20-525 3681
>> <mailto:loet@leydesdorff.net> loet@leydesdorff.net;
>> <http://www.leydesdorff.net/> http://www.leydesdorff.net
>>
>> -----Original Message-----
>> From: fis-bounces@listas.unizar.es [mailto:fis-bounces@listas.unizar.es]
>> On Behalf Of Michel Petitjean
>> Sent: Monday, April 05, 2004 9:15 AM
>> To: fis@listas.unizar.es
>> Subject: [Fis] FIS / introductory text / 5 April 2004
>>
>>
>> 2004 FIS session introductory text.
>>
>> Dear FISers,
>>
>> I would like to thank Pedro Marijuan for his kind invitation
>> to chair the 2004 FIS session. The session is focussed on "Entropy and
>> Information". It is vast, that I am afraid to be able only to evoke some
>> general aspects, discarding specific technical developments.
>>
>> Entropy and Information: two polymorphic concepts.
>>
>> Although these two concepts are undoubtly related, they have different
>> stories.
>>
>> Let us consider first the Information concept.
>> There was many discussions in the FIS list about the meaning
>> of Information. Clearly, there are several definitions.
>> The information concept that most people have in mind is outside the
>> scope of this text: is it born with Computer Sciences, or is it born
>> with Press, or does it exist since a so long time that nobody could date
>> it? Neglecting the definitions from the dictionnaries (for each language
>> and culture), I would say that anybody has his own concept. Philosophers
>> and historians have to look. The content of the FIS archives suggests
>> that the field is vast.
>>
>> Now let us look to scientific definitions. Those arising from
>> mathematics are rigorous, but have different meanings. An example is the
>> information concept emerging from information theory (Hartley, Wiener,
>> Shannon, Renyi,...). This concept, which arises from probability theory,
>> has little connections with the Fisher information, which arises also
>> from probability theory. The same word is used, but two rigorous
>> concepts are defined. One is mostly related to coding theory, and the
>> other is related to estimation theory. One deals mainly with non
>> numerical finite discrete distributions, and the other is based on
>> statistics from samples of parametrized family of distributions. Even
>> within the framework of information theory, there are several
>> definitions of information (e.g. see the last chapter of Renyi's book on
>> Probability Theory). This situation arises often in mathematics: e.g.,
>> there are several concepts of "distance", and, despite the basic axioms
>> they all satisfy, nobody would say that they have the same meaning, even
>> when they are defined on a common space.
>>
>> Then, mathematical tools are potential (and sometimes demonstrated)
>> simplified models for physical phenomenons. On the other hand,
>> scientists may publish various definitions of information for physical
>> situations. It does not mean that any of these definitions should be
>> confused between themselves and confused with the mathematical ones. In
>> many papers, the authors insist on the analogies between their own
>> concepts and those previously published by other authors: this attitude
>> may convince the reviewers of the manuscript that the work has interest,
>> but contribute to the general confusion, particularly when the confusing
>> terms are recorded in the bibliographic databases. Searching in
>> databases with the keyword "information" would lead to a considerable
>> number of hits: nobody would try it without constraining the search with
>> other terms (did some of you tried?).
>>
>> We consider now the Entropy concepts. The two main ones are the
>> informational entropy and the thermodynamical entropy. The first one has
>> non ambiguous relations with information (in the sense of information
>> theory), since both are defined within the framework of a common theory.
>> Let us look now to the thermodynamical entropy, which was defined by
>> Rudolf Clausius in 1865. It is a physical concept, usually introduced
>> from the Carnot Cycle. The existence of entropy is postulated, and it is
>> a state function of the system. Usual variables are temperature and
>> pressure. Entropy calculations are sometimes made discarding the
>> implicit assumptions done for an idealized Carnot Cycle. Here come
>> difficulties. E.g., the whole universe is sometimes considered as a
>> system for which the the entropy is assumed to have sense. Does the
>> equilibrium of such a system has sense? Does thermodynamical state
>> functions make sense here? And what about "the" temperature? These
>> latter variable, even when viewed as a function of coordinates and/or
>> time, has sense only for a restricted number of situations. These
>> difficulties appear for many other systems. At other scales, they may
>> appear for microscopic systems, and for macroscopic systems unrelated to
>> thermochemistry.
>> In fact, what is often implicitly postulated is that the thermodynamical
>> entropy theory could work outside thermodynamics.
>>
>> Statistical mechanics creates a bridge between microscopic and
>> macroscopic models, as evidenced from the work of Boltzmann. These two
>> models are different. One is a mathematical model for an idealized
>> physical situation (punctual balls, elastic collisions, distribution of
>> states, etc..), and the other is a simplified physical model, working
>> upon a restricted number of conditions. The expression of the entropy,
>> calculated via statistical mechanics methods, is formally similar to the
>> informational entropy. This latter has appeared many decades after the
>> former. Thus, the pioneers of information theory (Shannon, von Neumann)
>> who retain the term "entropy", are undoubtly responsible of the
>> historical link between <<Entropy>> and <<Information>> (e.g. see
>> http://www.bartleby.com/64/C004/024.html).
>>
>> Although "entropy" is a well known term in information theory, and used
>> coherently with the term "information" in this area, the situation is
>> different in science. I do not know what is "information" in
>> theermodynamics (does anybody know?). However, "chemical information" is
>> a well known area of chemistry, which covers many topics, including data
>> mining in chemical data bases. In fact, chemical information was
>> reognized as a major field when the ACS decided in 1975 to rename one of
>> its journals "Journal of Chemical Information and Computer Sciences": it
>> was previously named the "Journal of Chemical Documentation". There are
>> little papers in this journal which are connected with entropy
>> (thermodunamical of informational). An example is the 1996 paper of
>> Shu-Kun Lin, relating entropy with similarity and symmetry. Similarity
>> is itself a major area in chemical information, but I consider that the
>> main area of chemical information is related to chemical databases, such
>> that the chemical information is represented by the nodes and edges
>> graph associated to a structural formula. Actually, mathematical tools
>> able to work on this kind of chemical information are lacking,
>> particulary for statistics (did anyone performed statistics on graphs?).
>>
>> In 1999, the links between information sciences and entropy were again
>> recognized, when Shu-Kun lin created the open access journal "Entropy":
>> <<An International and Interdisciplinary Journal of Entropy and
>> Information Studies>>. Although most pluridisciplinary journals are at
>> the intersection of two areas, Shu-Kun Lin is a pionneer in the field of
>> transdisciplinarity, permitting the publication in a single journal of
>> works related to entropy and/or information theory, originating from
>> mathematics, physics, chemistry, biology, economy, and philosophy.
>>
>> The concept of information exists in other sciences for which the term
>> entropy is used. Bioinformation is a major concept in bioinformatics,
>> for which I am not specialist. Thus I hope that Pedro Marijuan would
>> like to help us to understand what are the links between bioinformation
>> and entropy. Entropy and information are known from economists and
>> philosophers. I also hope they add their voice to those of scientists
>> and mathematicians, to enlight our discussions during the session.
>>
>> Now I would like to draw some provocative conclusions. Analogies between
>> concepts or between formal expressions of quantities are useful for the
>> spirit, for the quality of the papers, and sometimes they are used by
>> modellers to demonstrate why their work merit funds (does anybody never
>> do that?). The number of new concepts in sciences (includes mathematics,
>> economy, humanities, and so on) is increasing, and new terms are picked
>> in our natural language: the task of the teachers becomes harder and
>> harder. Entropy and Information are like the "fourth dimension", one
>> century ago: they offer in common the ability to provide exciting topics
>> to discuss. Unfortunately, Entropy and Information are much more
>> difficult to handle.
>>
>> Michel Petitjean Email: petitjean@itodys.jussieu.fr
>> Editor-in-Chief of Entropy entropy@mdpi.org
>> ITODYS (CNRS, UMR 7086) ptitjean@ccr.jussieu.fr
>> 1 rue Guy de la Brosse Phone: +33 (0)1 44 27 48 57
>> 75005 Paris, France. FAX : +33 (0)1 44 27 68 14
>> http://www.mdpi.net http://www.mdpi.org
>> http://petitjeanmichel.free.fr/itoweb.petitjean.html
>> http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html
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>>
>>
>>
>>
>>
>

-- 
Dr. Shu-Kun Lin
Molecular Diversity Preservation International (MDPI)
Matthaeusstrasse 11, CH-4057 Basel, Switzerland
Tel. +41 61 683 7734 (office)
Tel. +41 79 322 3379 (mobile)
Fax +41 61 302 8918
E-mail: lin@mdpi.org
http://www.mdpi.org/lin/
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