Gibbs' Paradox and the definition of entropy

Entropy

Volumn 10, Issue 1, 2008, Pages 15-18

  Swendsen, Robert H ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Boltzmann; Entropy; Extensivity; Gibbs' Paradox

Indexed keywords

EID: 42149159638     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/entropy-e10010015     Document Type: Article

References (19)

1. Gibbs, J. W., On the Equilibrium of Heterogeneous Substances Transactions of the Connecticut Academy 1873, 3, 108-248, 343-524.
2. Gibbs, J. W. The Collected Works of J. W Gibbs; Yale University Press, 1948; Vol. 1.
3. Gibbs, J. W. Elementary Principles of Statistical Mechanics; Yale University Press: New Haven, 1902;
4. Reprinted by (Dover, New York, 1960), pp. 206-207.
5. Pathria, R. K. Statistical Mechanics, 2nd ed.; Butterworth-Heinemann: Boston, 1996; pp. 22-26.
6. See especially Eq. (1a), which agrees with Eq. 1 in this paper if the temperature is replaced by the energy as a variable.
7. Landau, L. D.; Lifshitz, E. M. Statistical Physics; Pergamon Press: New York, 1980; pp. 24-25.
8. Reif, F. Fundamentals of Statistical and Thermal Physics; McGraw-Hill: New York, 1965; pp. 243-245. This book and some others use a definition of the partition function that also leads to the traditional expression for the entropy.
9. Everett, D. H. Basic Principles of Colloid Science; Royal Society of Chemistry: London, 1988.
10. Boltzmann, L., Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht Wien. Ber. 1877, 76, 373-435
11. Reprinted in Wissenschaftliche Abhandlungen von Ludwig Boltzmann, Vol. II; Chelsea: New York, 1968; pp. 164-223.
12. Swendsen, R. H., Statistical mechanics of colloids and Boltzmann's definition of the entropy Am. J. Phys. 2006, 74, 187-190.
13. Swendsen, R. H., Statistical mechanics of classical systems of distinguishable particles J. Stat. Phys. 2002, 107, 1143-1165.
14. Planck, M., Über das Gesetz der Energieverteilung im Normal Spektrum Drudes Annalen 1901, 553-562
15. Reprinted in Ostwalds Klassiker der exakten Wissenschaften, Band 206, Die Ableitung der Strahlungsgesetze, pp. 65-74. The equation appears with an arbitrary additive constant on p. 68 of the reprinted text.
16. Planck, M. Theorie der Wärmestrahlung; J. A. Barth: Leipzig, 1906;
17. Translated into English by Morton Masius in M. Planck, The Theory of Heat Radiation; Dover: New York, 1991; p. 119.
18. Jaynes, E. T. The Gibbs Paradox. In Maximum-Entropy and Bayesian Methods; Erickson, G., Neudorfer, P., Smith, C. R., Eds.; Kluwer: Dordrecht, 1992; pp 1-22.
19. Ben-Naim, A., On the So-Called Gibbs Paradox, and on the Real Paradox Entropy 2007, 9, 133-136.