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Ugly SymmetryRevised Information Theoryand Its Application Shu-Kun Lin www.mdpi.org/lin/ A talk @ ACS Meeting 4 April 2001
Technical Intelligence • Info searching, info analysis, decision making • What is information?Relation with other concepts:similarity, diversity..., entropy, symmetry • Quantitative assessmentInformation Theory (IT)
Matter–Energy–Information Consider chemistry as an information science. ... ...bringing forward in chemistry the 3rd component of the basic trilogy of the matter-energy-information. – Jean-Marie Lehn, 2000 • Information - Symmetry • Information - Entropy • Information - Stability(Information Theory - Thermodynamics)(The Three Laws? The Three Laws)
However, the existing relationships are either confusing or wrong Statistical mechanics Group theoryentropy symmetry -Higher symmetry-higher order, lower entropy Prigogine‘s Order out of ChaosGibbs paradox of mixing (ws - symmetry number) Incorrect!It is incorrect to compare the stability and the symmetry of a dynamic system (a gas) and a static structure (crystal).
Information theoryrelationship of entropy S -information I Regarding the term “entropy”, “My greatest concern was what to call it. I thought of calling it ‘uncertainty’. When I discussed it with John von Neumann, he had a better idea: ‘You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one knows what entropy really is, so in a debate you will always have the advantage’ ” -von Neumann’s private communication with Shannon We must revise IT
Information theory Lewis' remark:"gain of entropy means loss of information, nothing more......" • Lewis, G. N. (1930) Science 71, 569 Three laws of information theory?
The First Lawof Information Theory The logarithmic function L (or the sum of entropy and information) of an isolated system remains unchanged. The First Law of ThermodynamicsF-Helmholtz free energy (Helmholtz potential) The first law e.g., a 1.44MB disk, L=1.44MB whether the disk is empty or occupied with a file of the size of 1.44MB. Let us use any available compression method to reduce the size of the original file to 0.40MB. Then, I=0.40MB and S=1.04MB and L=1.44MB .
2nd Lawof Information Theory(constant L=S+I ) Information I of an isolated system decreases to a minimum at equilibrium. Or: for an isolated system, entropy S increases to a maximum at equilibrium. 2nd Law of Thermodynamics The second law
The function L of the universe is a constant.L=S+I The entropy S of the universe tends toward a maximum. Information theory The energy E of the universe is a constant. The entropy S of the universe tends toward a maximum. ClausiusThermodynamics universe = system + surroundings
The third Lawof Information Theory For a perfect crystal (at zero absolute thermodynamic temperature), the information is zero and the static entropy is at the maximum. Defines static entropy The third Law Thermodynamics For a perfect crystal (at zero absolute thermodynamic temperature), the entropy is zero. Defines entropy The third law
A more general form of the third law of information theory “for a perfect symmetric static structure, the information is zero and the static entropy is the maximum”. - low temperature - chemical reaction form static structure (a molecule): bond formation (connectivity) – staticsupramolecular structure - static - self-organizationprotein folding - static - self-assembling (many molecules)
Symmetry nonsymmetry indistinguishabilitydistinguishability the same different Similarity
Similarity - Incomplete Symmetry http://www.cindy.com/ Incomplete bilateral symmetry Earth is not a perfect sphere
Entropy - information Symmetry - nonsymmetryS I Symmetry number nonsymmetry number Similarity (imperfect symmetry)
The Similarity Principle • The higher the similarity among the components is, the higher the value of entropy will be and the higher the stability will be.
The Similarity Principle If all the other conditions remain constant, the higher the similarity among the componentsis, the higher value of entropy of mixing, assembling or chemical bond formation process will be. The higher the similarity among the components is, the more spontaneous the mixing, the assembling or the chemical bond formation process will be, and the more stable the mixture, the assemblage or the chemical bond will be. Lin, S.-K. (1997) Theorochem J. Mol. Struct.398, 145-153
Gibbs Paradox of Entropy of Mixing Entropy of mixing decreasesdiscontinuously with similarity. (DS)distinguishable =2R ln 2=11.53 JK–1 (DS)indistinguishable =0 -distinguishable or nonsymmetry -the same or not the same -either symmetry or nonsymmetry
Curie-Rosen-symmetry principle • The effects are more symmetric than the causes. (Curie) • For an isolated system the degree of symmetry cannot decrease as the system evolves, but either remains constant or increases. (Rosen) We have proved it (the 2nd law of IT and the similarity principle) A special case of the similarity principle
Symmetry definedSymmetry as a Greek word exactly means “same measure”or measure of indistinguishabilityrotational symmetrytranslational symmetrybilateral symmetrypermutation symmetry… invariant transformations “microstates” of the same propertydynamic symmetry - static symmetry
Nonsymmetric state Symmetric state Static symmetry
Ugly Symmetry-Beautiful DiversityMolecular Diversity Preservation Internationalwww.mdpi.net -to preserve permanently historically significant research chemical samples in the chemical museum in Basel, Switzerland -to share and exchange any other rare chemical samples worldwide -founded in 1996 in Basel, Switzerland
MoleculesA Journal of Synthetic Chemistry and Natural Product Chemistry ISSN 1420-3049 • Is an e-journal now in its 6th successful year of publication, available through free subscription at the Molecules website: • http://www.mdpi.org/molecules/
Similarity rule a component in a molecular recognition process loves others of like properties. hydrophobic interaction p-stacking in DNA similarity in softness of the well-known hard-soft-acid-base rules) predicts the affinity of individuals of similar properties Complementarity rule predicts the affinity of individuals of certain contrast properties. negative charge-positive charge, donor-acceptor, convex and concave final structure is more "complete", more integral, more “solid” and more symmetric due to the property offset of the components Similarity Rule and Complementarity Rule
Similarity rulePhase separationpermutation symmetry Separation of two tataric acid enantiomers LLLLLLLL LLLLLLLL LLLLLLLL DDDDDDD DDDDDDD DDDDDDD - Louis Pasteur
Symmetry and beauty Nature1998, 396, 321-322 also Nature1994,368, 239-42 Facial shape and judgements of female attractiveness.
Ugly Symmetry A view of the earth
Ugly Symmetry Stereochemical representation with false mirror symmetry: Both wedges have the thick ends at R3 and R4 placed identically away from the center Shu-Kun Lin, Luc Patiny, Andrey Yerin, Janusz L. Wisniewski and Bernard Testa. Enantiomer 2000, 5, 571-583. However, none of the drugs (pharmaceuticals) discovered so far are very symmetric. Very few bioactive compounds are symmetric.
The highly symmetric paintings like this one found in manyfamous modern art museums are the emperor's new clothes.
Conclusion Information loss – entropy - Symmetry (Information Theory-Thermodynamics)The Three Laws Chemical processes: information, entropy and symmetry evolution can be considered Higher symmetry – higher stability (good) Higher symmetry – higher information loss (bad) Beauty =stability+information