Correlation of entropy with similarity and symmetry

Journal of Chemical Information and Computer Sciences

Volumn 36, Issue 3, 1996, Pages 367-376

  Lin, Shu Kun ^a,b  

^a CIBA GEIGY LTD   (Switzerland)

^b Molec Diversity Preservation Intl   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0043137169     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci950077k     Document Type: Article

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2. 1
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25. 12 can be treated as a proper operation or transformation which may make a contribution to the entropy, because such an inversion is very similar to the racemization (which has an effect of entropy increase, see: Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates, and Resolutions; Wiley: New York, 1981; p 47.) of enantiomers due to the inversion. It should be emphasized that it is not the specific type of transformation (rotation or permutation or whatever else) that determines the symmetry number of the system. The rotation, which is the only transformation regarded as the proper operation so far, can also become strictly hindered, resulting in rotational isomers, see: Oki, M. The Chemistry of Rotational Isomers; Springer-Verlag: Berlin, 1993.
26. 12 can be treated as a proper operation or transformation which may make a contribution to the entropy, because such an inversion is very similar to the racemization (which has an effect of entropy increase, see: Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates, and Resolutions; Wiley: New York, 1981; p 47.) of enantiomers due to the inversion. It should be emphasized that it is not the specific type of transformation (rotation or permutation or whatever else) that determines the symmetry number of the system. The rotation, which is the only transformation regarded as the proper operation so far, can also become strictly hindered, resulting in rotational isomers, see: Oki, M. The Chemistry of Rotational Isomers; Springer-Verlag: Berlin, 1993.
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108. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
109. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
110. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
111. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
112. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
113. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
114. The resolutions of this paradox has been very controversial. Some recent debates are: Lesk, A. M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114. van Kampen, N. G. The Gibbs Paradox, In Essays in Theoretical Physics: Parry, W. E., Ed.: Pergamon: Oxford. 1984, 303-312. Kemp, H. R. Gibbs' paradox for entropy of mixing. J. Educ. Chem. 1985, 62, 47-49. Kemp, H. R. Gibbs' paradox: Two views on the correction term. J. Educ. Chem. 1986, 63, 735-736. Dieks, D.; van Dijk, V. Another look at the quantum mechanical entropy of mixing. Am. J. Phys. 1988, 56, 430-434. Richardson, I. W. The Gibbs paradox and unidirectional fluxes. Eur. Biophys. J. 1989, 17, 281-286; Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Der. Bunsen-Ges. Phys. Chem. 1991, 94, 537.
115. This phenomenon is observed and the corresponding technique of unit operation is used routinely in solid chemicals production plants.
116. (a) See ref 12b.
117. (b) Zee, A. Fearful Symmetry, The Search for Beauty in Modern Physics; Collier Books: New York, 1986; p 13.
118. Cornforth, J. W. Asymmetry and Enzyme Action; The Nobel prize in chemistry lecture, In J. Mol. Catal. 1975-1976, 1, pp 145-157.
119. 77
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122. For example, the treatment of degenerated intramolecular processes depicted in Figure 1a.
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126. "Die Energie der Welt ist constant. Die Entropie der Welt strebt einem Maximum zu". See: Clausius, R. Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. Ann. Phys. 1865, 125, 353-400; especially p 400.