Gibbs paradox

Gibbs paradox and its resolutions (http://www.mdpi.org/lin/entropy/gibbs-paradox.htm)

The resolution of this paradox has been very controversial. A list of papers mainly published in journals on this topic is compiled. Comments are welcomed. Please write me (E-mail: [email protected]) if you have a paper to be listed here or if you have any suggestion. I have a collection of almost all papers in pdf format.

Journal Papers and Book Chapters

Gibbs, J.W. Scientific Papers. 1906. (PDF version 32 MB, available at http://www.archive.org/details/scientificpapers01gibbuoft. (PDF, 23 MB).
Gibbs, J.W. Elementary Principles in Statistical Mechanics. 1902. (PDF version 32 MB, available at http://www.archive.org/details/elementaryprinci00gibbrich. Reprinted version, New York; (1981) Woodbridge, CT: Ox Bow Press ISBN 0-918024-20-X.
Schrödinger, E. Isotopie und Gibbssches Paradoxon. Zeitschrift für Physik A Hadrons and Nuclei 1921, 5 (2-3), 163-166. DOI 10.1007/BF01329248. http://www.springerlink.com/content/r615226147x44628/
Watson, D.L. Biological Organization. The Quarterly Review of Biology 1931, 6 (2), 143-166.
Keywords: G. N. Lewis: Gain of entropy means loss of information
Born, M. Max Karl Ernst Ludwig Planck. 1858-1947. Obituary Notices of Fellows of the Royal Society 1948, 6 (17), 161-188.
Keywords: experimental resolution of Gibbs's paradox in 1922: Uber die freie Energie von Gasmolekiilen mit beliebiger Geschwindigkeitsverteilung. S. B. preuss. Akad. Wiss. pp. 63-70.
Onsager, L. The effects of shape on the interaction of colloidal particles. Annals of the New York Academy of Sciences 1949, 51 (4) , 627–659. doi:10.1111/j.1749-6632.1949.tb27296.x
Keywords: a most often cited theory of demixing
Rothstein, J. Information, Measurement, and Quantum Mechanics. Science 1951, 114, 171-175.
Landé, A. Continuity, A Key to Quantum Mechanics. Philosophy of Science 1953, 20 (2), 101-109.
Lande, A. The Logic of Quanta. The British Journal for the Philosophy of Science 1956, 6 (24), 300-320.
Keywords: entropy-continuity, fractional equality (a degree of fractional equality between two states signifies a corresponding degree of 'fractional separability' of the two state), mechanical conjugacy; degeneracy, symmetry, Third Law
Klein, M. J. Note on a Problem Concerning the Gibbs Paradox. Amer. J. Phys. 1958, 26 (2), 80-81.
Falk, G. Third Law of Thermodynamics. Phys. Rev. 1959, 115, 249-253. DOI: 10.1103/PhysRev.115.249
Grad, H. The Many Faces of Entropy. Communications on Pure and Applied Mathematics. 1961, 14, 232-354. (available at http://doi.wiley.com/10.1002/cpa.3160140312)
Noyes, R.M. Entropy of Mixing of Interconvertible Species. Some Reflections on the Gibbs Paradox. Journal of Chemical Physics 1961, 34 (6): 1983-1985.
Varshavsky, Yu.S.; Sheinin, A.B. On the entropy of systems containing poorly distinguishable components. Dokl. Akad. Nauk SSSR 1963, 148 (5), 1099–1101. Russian version.
Rosen, R. The Gibbs Paradox and the Distinguishability of Physical Systems. Philosophy of Science 1964, 31, 232-236.
Landé, A. Discussion: Solution of the Gibbs Entropy Paradox. Philosophy of Science 1965, 32 (2), 192-193.
Fong, P. Semipermeable Membrane and the Gibbs Paradox. American Journal of Physics 1964, 32 (2), 170-171.
Fay, G. Notes on the quantum-mechanical discussion of the Gibbs paradox. Acta physica Academiae Scientiarum Hungaricae 1965, 18(4), 273-283. DOI 10.1007/BF03156446. http://www.springerlink.com/content/t6v0jn5t33500882/
Ionescup, N.J. Complete Solution of Gibbs Paradox. Studii si Cercetari de Fizica 1968, 20 (9) 927-?. (English paper) found in Web of Science.
Boyer, T.H. Sharpening Bridgman's Resolution of the Gibbs Paradox. American Journal of Physics 1970, 38 (6): 771-773.
Penrose, O. Fundations of Statistical Mechanics, Dover, New York, 1970, pp. 171-172.
Lyuboshits, V. L.; Podgoretskii, M. I. Entropy of a Polarized Gas and the Gibbs Paradox. Soviet Physics Doklady 1971, 15, 858.
Alexanian, M. Gibbs paradox in particle physics. Physical Review D. 1971, 4, 2432-2439.
Lyuboshits, V. L.; Podgoretskii, M. I. The Gibbs Paradox. Physics-Uspekhi 1972, 14 (5), 662-666. (http://www.turpion.org/php/paper.phtml?journal_id=pu&paper_id=4676)
Casper, B.M.; Frerer, S. "Gibbs paradox" paradox. Amer. J. Phys. 1973, 41, 509.
Bazarov, I.P. Gibbs paradox and its experimental detection. Russian Physics Journal 1973, 16 (12), 1715-1718. (Translated from Izvestiya VUZ. Fizika, No. 12, pp. 110–114, December, 1973. Available at http://www.springerlink.com/content/t6284114344x5171/).
Bazarov, I.P. Einstein's paradox and a new mixing paradox. Russian Physics Journal 1975, 18 (5), 626-629.
(Translated from Izvestiya Vysshikh Uehebnykh Zavedenii, Fizika, No. 5, pp. 39–43, May, 1975. Available at http://www.springerlink.com/content/kw8m8128k50576r7/).
Sklar, L. Thermodynamics, Statistical Mechanics and the Complexity of Reductions. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1974, 15-32.
Keywords: Gibbs's paradox (page 23)
Varshavsky, Yu.S.; Sheinin, A.B. Discussion of Gibbs paradox. Zhurnal Fizicheskoi Khimii 1975, 49 (2), 564-564.
Gelfer, M.; Luboshitz, V. L.; Podgoretskii, M. I. Gibbs Paradox and Identity of Particles in Quantum Mechanics; Moscow: Nauka, 1975 (monograph in Russian).
Leinaas, J.M.; Myrheim, J. On the theory of identical particles. Il Nuovo Cimento B (1971-1996), 1977, 37 (1), 1-23.
Biot, M.A. New Fundamental Concepts and results in thermodynamics with chemical applications. Chemical Physics 1977, 22, 183-198. (listed as paper 156 at http://www.pmi.ou.edu/Biot2005/biotConferenceBiotsPapers.htm).
Biot, M.A. Variational-Lagrangian irreversible thermodynamics of initially-stressed solids with thermomolecular diffusion and chemical reactions. Journal of the Mechanics and Physics of Solids 1977, 25, 289-307, and Errata, vol. 26, pp. 59, 1978. (listed as paper 157 at http://www.pmi.ou.edu/Biot2005/biotConferenceBiotsPapers.htm). See in particular page 291.
Biot, M.A. New Variational-Lagrangian Thermodynamics of Viscous Fluid Mixtures with Thermomolecular Diffusion. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 1979, 365, 467-494. (listed as paper 163 at http://www.pmi.ou.edu/Biot2005/biotConferenceBiotsPapers.htm).
Keywords: new theory to avoid difficulty of Gibbs paradox
Lavis, D. The Role of Statistical Mechanics in Classical Physics. The British Journal for the Philosophy of Science 1977, 28 (3), 255-279.
Keywords: to avoid the diiculties of Gibbs's paradox
Landsberg, P. T.; Tranah; D. The Gibbs Paradox and Quantum Gases. Am. J. Phys. 1978, 46 (3), 228-230.
Lesk, A.M. On the Gibbs paradox: what does indistinguishability really mean? J. Phys. A: Math. Gen. 1980, 13, L111-L114.
Grandy, W.T., Jr. Indistinguishability, symmetrisation and maximum entropy. Eur. Phys. J. 1981, 2, 86.
Gough, W.; Richards, J.P.G. Distinguishability in the teaching of statistical mechanics. Eur. J. Phys. 1981, 2, 82-85.
Penrose, O. Entropy and Irreversibility. Annals of the New York Academy of Sciences 1981, 373 (1) , 211–219; http://www.blackwell-synergy.com/doi/abs/10.1111/j.1749-6632.1981.tb51149.x
Varshavsky, Yu.S.; Sheinin, A.B. Gibbs on the "Gibbs paradox". Problems of the History of Science and Technology 1983 (1), 68-75. Russian version.
van Kampen, N.G. The Gibbs Paradox, In: Essays in Theoretical Physics; Parry, W. E., Ed.; Pergamon: Oxford, 1984, pages 303-312.
Kemp, H.R. Gibbs' paradox for entropy of mixing. J. Chem. Educ. 1985, 62, 47-49.
Gubin, V.B. Some requirements to the right solution of Gibbs paradox. Zhurnal Fizicheskoi Khimii 1985, 59 (2), 517-520.
McDonald, J. J. Gibbs' paradox: Two views on the correction term. J. Chem. Educ. 1986, 63, 735.
Kemp, H.R. Gibbs' paradox: Two views on the correction term. J. Chem. Educ. 1986, 63, 736.
Keesing, R. G. Lost work and the entropy of mixing. Eur. J. Phys. 1986, 7, 266-268; doi: 10.1088/0143-0807/7/4/009
Ben-Naim, A. Is mixing a thermodynamic process? Amer. J. Phys. 1987, 55, 725.
Mehra, J. Erwin Schrödinger and the rise of wave mechanics. II. The creation of wave mechanics. Foundations of Physics 1987, 17 (12), 1141-1188. (Gibbs paradox and quantum mechanics.) http://www.springerlink.com/content/u517616764461837/
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. (Available at www.springerlink.com/index/H82402636K54N35N.pdf)
Rössler, O.E. Symmetry-Induced Disappearance of Reality: The Leibniz Effect. Leonardo 1989, 22 (1, Art and the New Biology: Biological Forms and Patterns), 55-59.
Lin, S.-K. Gibbs paradox and its resolutions. Ziran Zazhi 1989, 12, 376-379. A review in Chinese:
林树坤; 吉布斯悖论及其解 [J];自然杂志; 1989年12卷5期; 376-379.
Biedenharn, L.C.; Truini, P.; van Dam, H. A remark on possible violations of the Pauli principle. J. Phys. A: Math. Gen. 1989, 22, L67-L71.
Denbigh, K. G.; Redhead; M. L. G. Gibbs' paradox and non-uniform convergence. Synthese 1989, 81 (3), 283-313. (Available at http://www.springerlink.com/content/m166245626440308/)
Wantke, K.-D. A remark on the Gibbs-paradox of the entropy of mixing of ideal gases. Ber. Bunsen-Ges. Phys. Chem. 1991, 94, 537. (Only an abstract was ever published.)
Pesic, P.D. The principle of identicality and the foundations of quantum theory. I. The Gibbs paradox. American Journal of Physics 1991, 59, (11) 971-974.
Pesic, P.D. The principle of identicality and the foundations of quantum theory. II. The role of identicality in the formation of quantum theory. American Journal of Physics 1991, 59 (11), 975-979.
Price, H. Book Review: Entropy in Relation to Incomplete Knowledge by K. G. Denbigh; J. S. Denbigh, The Physical Basis of the Direction of Time by H. D. Zeh. Brit. J. Phil. Sci. 1991, 42, 111-144.
Jaynes, E.T. The Gibbs Paradox, In Maximum Entropy and Bayesian Methods; Smith, C. R.; Erickson, G. J.; Neudorfer, P. O., Eds.; Kluwer Academic: Dordrecht, 1992, p.1-22 (pdf file 206K). Also in postscript (72Kb) (http://bayes.wustl.edu/etj/node1.html).
Levitin, L.B. Gibbs Paradox And Equivalence Relation Between Quantum Information And Work. Physics and Computation, 1992. PhysComp'92., Workshop on, 1992 - ieeexplore.ieee.org.
Werner, R.F. The Free Quon Gas Suffers Gibbs' Paradox. Phys. Rev. D 1993, 48, 2929-2934.
Goodison, J.W.; Toms, D.J. The canonical partition function for quons. Physics Letters A 1994, 195, 38-42. arXiv:hep-th/9410096.
Beghian, L.E. Maxwell's demon revisited. Il Nuovo cimento. B 1994, 109 (6), 611-616. http://www.springerlink.com/content/r508881370168405/
Mosini, V. Fundamentalism, antifundamentalism, and Gibbs' paradox. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, Volume 26, Issue 2, August 1995, Pages 151-162.
Blumenfeld, L.A.; Grosberg, A.Y. Gibbs paradox and the notion of construction in thermodynamics and statistic physics. Biofizika 1995, 40, 660-667; English translation:
Blyumenfel'd, L. A.; Grosberg, A.Y. Gibbs' paradox and the concept of the construction of the system in thermodynamics and statistical physics. Biophysics 1995, 40 (3), 653-660.
Lee, M.H. Chemical potential: Gibbs-Duhem approach. Phys. Rev. E 1996, 53, 5488 - 5490.
Warren, P. Statistical Mechanics of Polydispersity, Combinatorial Entropy, and the Gibbs Paradox. An abstract.
Warren, P.B. Combinatorial Entropy and the Statistical Mechanics of Polydispersity. Phys. Rev. Lett. 1998, 80, 1369-1372. (Erratum. Phys. Rev. Lett. 1998, 80, 3671-3671). ("A simple entropic contribution to the free energy is identified from combinatorial considerations").
Lin, S.-K. Correlation of Entropy with Similarity and Symmetry. Journal of Chemical Information and Computer Sciences 1996, 36, 367-376.
Lin, S.-K. Molecular Diversity Assessment: Logarithmic Relations of Information and Species Diversity and Logarithmic Relations of Entropy and Indistinguishability After Rejection of Gibbs Paradox of Entropy of Mixing. Molecules 1996, 1, 57-67.
Lin, S.-K. Gibbs paradox of entropy of mixing: Experimental facts, its rejection, and the theoretical consequences. Electronic Journal of Theoretical Chemistry 1996, 1, 135-150.
Lin, S.-K. Understanding structural stability and process spontaneity based on the rejection of the Gibbs paradox of entropy of mixing. Theochem-Journal of Molecular Structure 1997, 398, 145-153.
Navarro, L. Gibbs, Einstein and the Foundations of Statistical Mechanics. Arch. Hist. Exact Sci. 1998, 53, 147–180
Harrison, S.; Dunham, P. Decoherence, Quantum Theory and Their Implications for the Philosophy of Geomorphology. Transactions of the Institute of British Geographers, New Series 1998, 23 (4), 501-514.
Needham, P. What is Water? Analysis 2000, 60 (265), 13-21. doi:10.1111/1467-8284.00197.
Styer, D.F. Insight into entropy. American Journal of Physics 2000, 68 (12), 1090-1096.
Brown, H. R.; Sjoeqvist, E.; Bacciagaluppi, G. Remarks on identical particles in de Broglie-Bohm theory. Phys. Lett. A 1999, 251, 229-235.
Smith, J.D.H. Some Observations on the Concepts of Information-Theoretic Entropy and Randomness. Entropy 2001, 3, 1-11.
Lin, S.-K. The Nature of the Chemical Process. 1. Symmetry Evolution – Revised Information Theory, Similarity Principle and Ugly Symmetry. Int. J. Mol. Sci. 2001, 2, 10-39. arXiv:physics/0105024
Hansson, T.H.; Isakov, S. B.; Leinaas, J. M.; Lindström, U. Classical phase space and statistical mechanics of identical particles. Phys. Rev. E 2001, 63, 026102 [15 pages]. arXiv:quant-ph/0003121.
Scherer, L.G.-C. La paradoja de Gibbs. Journal of the Mexican Chemical Society 2001, 45, 145-148. http://redalyc.uaemex.mx/redalyc/pdf/475/47545402.pdf. In Spanish.
Swendsen, R.H. Statistical mechanics of classical systems with distinguishable particles. Journal of Statistical Physics 2002, 107 (5-6), 1143-1166.
Tseng, C.-Y.; Caticha, A. Yet another resolution of the Gibbs paradox: an information theory approach. (Presented at MaxEnt 2001, the 21th International Workshop on Bayesian Inference and Maximum Entropy Methods (August 4-9, 2001, Baltimore, MD, USA)). p. 331 in "Bayesian Inference and Maximum Entropy Methods in Science and Engineering" ed. by R. L. Fry (A.I.P. Vol. 617, 2002).
Das, S.K.; Sengupta, S. Extensivity of entropy. Indian Journal of Pure and Applied Physics 2003, 41 (12), 941-945. (See also: Home, D.; Sengupta, S. Extensivity of entropy and modern form of Gibbs paradox. Pramana 1981, 17, 509-514.)
Muller, I. Considerations about the Gibbs paradox. In: Waves and Stability in Continuous Media, Proceedings of the 12th Conference on WASCOM 2003: pages 341-351, 2004. Editors: Monaco, R.; Pennisi, S.; Rionero, S.; Ruggeri, T. (Conference Information: 12th Conference on Waves and Stability in Continuous Media, Villasimius, ITALY, JUN 01-07, 2003).
http://eproceedings.worldscinet.com/9789812702937/9789812702937_0040.html
French, S.R.D.; Rickles, D.P. Understanding Permutation Symmetry. In "Symmetries in physics: philosophical reflections", edited by Katherine Brading and Elena Castellani, Cambridge University Press, 2003.
Almeida, M.P. Thermodynamical entropy (and its additivity) within generalized thermodynamics. Physica A: Statistical Mechanics and its Applications 2003, 325 (3-4), 426-438. doi:10.1016/S0378-4371(03)00262-0
Estrada, E.; Avnir, D. Continuous Symmetry Numbers and Entropy. J. Am. Chem. Soc. 2003, 125 (14), 4368 -4375; Mayer, J. E.; Brunauer, S.; Mayer, M. G. The Entropy of Polyatomic Molecules and the Symmetry Number. J. Am. Chem. Soc. 1933, 55, 37-53; DOI: 10.1021/ja01328a004.
Spencer, J.N.; Lowe, J.P. Entropy: The effects of distinguishability. Journal of Chemical Education 2003, 80 (12), 1417-1424.
Weinstein, S. Objectivity, Information, and Maxwell's Demon. Philosophy of Science 2003, 70, 1245–1255. http://philsci-archive.pitt.edu/archive/00002390/
Paty, M. The concept of quantum state: new views on old phenomena. A. Ashtekar et al. (eds.). Revisiting the Foundations of Relativistic Physics. 2003 Kluwer Academic Publishers: Printed in the Netherlands. http://www.scientiaestudia.org.br/associac/paty/
Keywords: indistinguishability, Einstein
Nagle, J.F. Regarding the Entropy of Distinguishable Particles. Journal of Statistical Physics 2004, 117, 1047-1062.
Swendsen, R.H. Response to Nagle’s Criticism of My Proposed Definition of the Entropy. Journal of Statistical Physics 2004, 117, 1063-1079.
Qian, H.; Elson, E.L.; Wolynes, P.G. Fluorescence Correlation Spectroscopy with High-Order and Dual-Color Correlation to Probe Nonequilibrium Steady States. Proceedings of the National Academy of Sciences of the United States of America 2004, 101 (9), 2828-2833.
Keywords: Identifiability, Signal Specificity
Remacle, F.; Levine, R.D. Quasiclassical Computation. Proceedings of the National Academy of Sciences of the United States of America 2004, 101 (33), 12091-12095.
Breuer, J.; Avnir, D. Continuity in symmetry and in distinguishability of states: The symmetry numbers of nonrigid molecules. Journal of Chemical Physics 2005, 122, 074110.
Kumar, N. Bose–Einstein condensation: Where many become one and so there is plenty of room at the bottom. Current Science 2005, 89 (12), 2093-2100.
Rosen, J. The Symmetry Principle. Entropy 2005, 7(4), 308-313.
Balian, R. Information in statistical physics. Stud. Hist. Phil. Mod. Phys. 2005, 36, 323-353. http://ipht.cea.fr/DocsphtV2//search/article.php?IDA=1194, arXiv:cond-mat/0501322
Hutter, K. Thermodynamics of polycrystalline materials within the theory of mixtures with continuous diversity. Geophysical Research Abstracts 2005, 7, 02210. An abstract. See Faria's PhD Thesis.
Mana, P. G. L.; Maansson, A.; Bjoerk, G. On distinguishability, orthogonality, and violations of the second law: contradictory assumptions, contrasting pieces of knowledge. (http://arxiv.org/abs/quant-ph/0505229/).
Haitun, S. D. The History of the Gibbs Paradox; Moscow: KomKniga, 2005 (monograph in Russian).
Enders, P. Equality and Identity and (In)distinguishability in Classical and Quantum Mechanics from the Point of View of Newton's Notion of State, 6th Int. Symp. Frontiers of Fundamental and Computational Physics, Udine, Italy, 26-29 Sept. 2004; in: Sidharth, B.G.; Honsell, F.; DeAngelis, A.(Editors), Frontiers of Fundamental Physics 2006, 239-245., Dordrecht: Springer.
Allahverdyan, A.E.; Nieuwenhuizen, T.M. Explanation of the Gibbs paradox within the framework of quantum thermodynamics. Physical Review E 2006, 73 (6), Art. No. 066119. (http://link.aps.org/abstract/PRE/v73/e066119).
Saunders, S. On the explanation for quantum statistics. Studies in History and Philosophy of Modern Physics 2006, 37 (1), 192-211.
Swendsen, R. H. Statistical mechanics of colloids and Boltzmann's definition of the entropy. Am. J. Phys. 2006, 74, 187-190.
Ben-Naim, A. The entropy of mixing and assimilation: An information-theoretical perspective. Am. J. Phys. 2006, 74, 1126-1135.
Faria, S.H. Creep and recrystallization of large polycrystalline masses. I. General continuum theory. Proc. R. Soc. A 2006, 462, 1493–1514. doi:10.1098/rspa.2005.1610.
Faria, S.H. Creep and recrystallization of large polycrystalline masses. II. Constitutive theory for crystalline media with transversely isotropic grains.. Proc. R. Soc. A 2006, 462, 1699–1720. 10.1098/rspa.2005.1635.
Faria, S.H. Creep and recrystallization of large polycrystalline masses. III. Continuum theory of ice sheets. Proc. R. Soc. A 2006, 462, 2797–2816. doi:10.1098/rspa.2006.1698.
Pdf files received from Dr. Faria on 14 April 2008.
Diósi, L.; Feldmann, T.; Kosloff, R. On exact identity between thermodynamic and informatic entropies in a unitary model of friction. International Journal of Quantum Information 2006, 4 (1), 99–104. (The reprint is also available at http://www.rmki.kfki.hu/~diosi/pub.html or here).
Uffink, J. Compendium of the foundations of classical statistical physics - Philosophy of Science Archive, 2006 - philsci-archive.pitt.edu. particularly page 81. (Chapter for "Philosophy of Physics", J. Butterfield and J. Earman (eds) 2007, ISBN: 978-0-444-51560-5).
Ben-Naim, A. On the So-Called Gibbs Paradox, and on the Real Paradox. Entropy 2007, 9, 132-136.
Lekner, J. Young Einstein and the beginnings of quantum mechanics. New Zealand Science Review 2007, 64 (1), 11-19. http://www.victoria.ac.nz/scps/staff/johnlekner/
Kiefer, C.; Kolland, G. Gibbs' paradox and black-hole entropy. 2007. arXiv:0707.0615v1 [gr-qc]; Kiefer, C.; Kolland, G. Gibbs' paradox and black-hole entropy. General Relativity and Gravitation 2008, 40 (6), 1327-1339; DOI 10.1007/s10714-008-0609-5.
Neumaier, A. On the foundations of thermodynamics. http://arxiv.org/pdf/0705.3790
Moroi, Y. Air/Solution interface and adsorption - Solution for the Gibbs paradox. Croatica Chemica Acta 2007, 80 (3-4), 381-394. Available from the publisher: http://hrcak.srce.hr/file/29067. (The "Gibbs paradox" mentioned in this paper is not really about entropy of mixing.)
Urusov, V.S. Gibbs paradox and symmetrization of a multicomponent system. Doklady Physical Chemistry 2007, 417 (Part 2), 337-341. (E-mail: [email protected])
Shafiee, A.; Karimi, M. On the relationship between entropy and information. General Relativity and Gravitation 2007. arXiv:quant-ph/0611061v2
Kozliak, E. I. Consistent Application of the Boltzmann Distribution to Residual Entropy in Crystals. Journal of Chemical Education 2007, 84, 493-498.
Enders, P. Is Classical Statistical Mechanics Self-Consistent? (A paper in honor of C. F. von Weizsäcker, 1912–2007). Progress in Physics 2007, 3, 85-87.
Lin, S.-K. Gibbs Paradox and the Concepts of Information, Symmetry, Similarity and Their Relationship. Entropy 2008, 10, 1-5. DOI: 10.3390/entropy-e10010001. arXiv:0803.2571v1 [physics.chem-ph].
Swendsen, R. H. Gibbs’ Paradox and the Definition of Entropy. Entropy 2008, 10, 15-18. DOI: 10.3390/entropy-e10010015.
Maslov, V. P. Solution of the Gibbs paradox in the framework of classical mechanics (Statistical Physics) and crystallization of the gas C₆₀. Mathematical Notes 2008, 83 (5-6), 716-722.
Maslov, V.P. New distribution formulas for classical gas, clusters, and phase transitions. Theoretical and Mathematical Physics 2008, 157(2), 1577-1594. DOI: 10.1007/s11232-008-0131-7.
Lin, S.-K. Gibbs Paradox and Similarity Principle. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conference Proceedings 1073. 2008, pages 49-60. Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Boraceia, Sao Paulo, Brazil, 6-11 July 2008. Editors: Marcelo de Souza Lauretto, Carlos Alberto de Bragança Pereira, Julio Michael Stern. Paper presented at MaxEnt2008. 2008, arXiv:0807.4314 [physics.gen-ph]. DOI: 10.1063/1.3039022. http://link.aip.org/link/?APCPCS/1073/49/1.
Kozliak, E.; Lambert, F.L. Residual Entropy, the Third Law and Latent Heat. Entropy 2008, 10, 274-284.
Paglietti, A. Thermal Radiation Effect in the Free Expansion of an Ideal Gas and Gibbs' Paradox in Classical Thermodynamics. arXiv:0901.1799 [pdf]; Paglietti, A. Interaction with thermal radiation in the free expansion and mixing of ideal gases and Gibbs' paradox in classical thermodynamics. arXiv:0904.4015v1 [physics.class-ph]. (Paglietti homepage: http://www.unica.it/~dis/Teachers/Paglietti.htm). (Paglietti homepage: http://www.unica.it/~dis/Teachers/Paglietti.htm)
Cheng, C.-H. Thermodynamics of the System of Distinguishable Particles. Entropy 2009, 11(3), 326-333; doi:10.3390/e11020326. http://arxiv.org/abs/0903.4748[pdf].
Maruyama, K.; Nori, F.; Vedral, V. Colloquium: The physics of Maxwell's demon and information. Reviews of Modern Physics 2009, 81(1) 1-23. [Also available at http://dml.riken.jp/~maruyama/]
Minkova, N.R. Finite Instrumental Resolution Scales in Plasma Modeling. Contrib. Plasma Phys. 2009, 49(1-2), 90 – 97. DOI 10.1002/ctpp.200910012.
Lee, S.H.; Pedrycz, W.; Sohn, G. Design of Similarity and Dissimilarity Measures for Fuzzy Sets on the Basis of Distance Measure. International Journal of Fuzzy Systems 2009, 11(2), 67-72. (The pdf file is downloadable from the journal website.)
Plasson, R.; Brandenburg, A. Homochirality and the need of energy. Arxiv preprint arXiv:0908.0658, 2009 - arxiv.org.
Chih-Yuan Tseng (National Central University). Abstract: X39.00007: Statistical mechanics rooted in maximum entropy method shows absence of the Gibbs paradox. http://meetings.aps.org/Meeting/MAR08/Event/81733.
Thomas V. Huynh (Naval Postgraduate School, Monterey, CA 93943), Xuan-Linh Tran (University of South Australia, Adelaide, South Australia, AU 5095) and John S. Osmundson. Architecting of Systems of Systems for Delivery of Sustainable Value. (Naval Postgraduate School, Monterey, CA 93943). Second International Symposium on Engineering Systems. MIT, Cambridge, Massachusetts, June 15-17, 2009. (http://esd.mit.edu/symp09/submitted-papers/huynh-paper.pdf).
Niven, R.K. Combinatorial entropies and statistics. Eur. Phys. J. B 2009, 70, 49–63. DOI: 10.1140/epjb/e2009-00168-5.
Enders, P. Gibbs’ Paradox in the Light of Newton’s Notion of State. Entropy 2009, 11, 454-456.
Wang, H.; Lee, S.; Kim, J. Quantitative Comparison of Similarity Measure and Entropy for Fuzzy Sets. (http://www.springerlink.com/content/v36405p022787455/).
Kozlov, V.V. Kinetics of collisionless gas: Equalization of temperature, growth of the coarse-grained entropy and the Gibbs paradox. Regular and Chaotic Dynamics 2009, 14(4-5), 535-540. DOI 10.1134/S1560354709040091. (http://www.springerlink.com/content/f2x0450g2474j4w4/).
Kozliak, E.I. Overcoming Misconceptions about Configurational Entropy in Condensed Phases. J. Chem. Educ. 2009, 86(9), 1063-1068.
Stepanov, I. A. Explanation of the Gibbs paradox in statistical mechanics. Physical Chemistry: An Indian Journal 2016, 11(2), 1-6.

Lecture Slides

Thermodynamics and the Gibbs Paradox. Presented by: Chua Hui Ying Grace, Goh Ying Ying, Ng Gek Puey Yvonne. http://sps.nus.edu.sg/~gohyingy/Thermodynamics.ppt. PPT file accessed on 4 April 2008.
Quantum thermodynamics view on the Gibbs paradox and work fluctuations. By Theo M. Nieuwenhuizen, University of Amsterdam, 26 October 2006. http://staff.science.uva.nl/~nieuwenh/QL2L.html. PPT file accessed on 4 April 2008.
Explanation of the Gibbs Paradox within the Framework of Quantum Thermodynamics. By Theo M. Nieuwenhuizen, University of Amsterdam, Physikalisches KolloquiumJohann Wolfgang Goete Universitaet, Frankfurt am Main, 31-01, 2007. http://staff.science.uva.nl/~nieuwenh/GibbsFrankfurt07.ppt. PPT file accessed on 4 April 2008.
Thermodynamics and Statistical Physics, Chapter 2 and Chapter 3. By W. Q. Cao, Hubei University, Wuhan, China. http://course.hubu.edu.cn/rt/ppt/Chapter%20II.ppt. PPT file accessed on 4 April 2008. In both English and Chinese.

Ph.D. Theses

1. Porta Mana, P.G.L. Studies in plausibility theory, with applications to physics. Ph.D. Thesis, 2007. The updated version with a few additional corrections, available at http://www.tp.umu.se/~mana/.

The following papers have been recommended by Dr. Porta Mana on 10 April 2008 for adding to this list:

Larmor, J. A Dynamical Theory of the Electric and Luminiferous Medium. Part III. Relations with Material Media. Proceedings of the Royal Society of London 1897, 61, 272-285. At §59 the Gibbs paradox is discussed.
Ehrenfest, P.; Trkal, V. Deduction of the dissociation-equilibrium from the theory of quanta and a calculation of the chemical constant based on this. Proc. Acad. Sci. Amsterdam (Proc. of the Section of Sciences Koninklijke Nederlandse Akademie van Wetenschappen) 1920, 23, 162-183.
Bridgman, P.W. The Nature of Thermodynamics (Harvard University Press, Cambridge, USA), first publ. 1941. http://www.archive.org/details/natureofthermody031258mbp PDF version, 8 MB. [See pp. 168-169].
Faria, S.H. Mixtures with continuous diversity: general theory and application to polymer solutions. Continuum Mech. Thermodyn. 2001, 13, 91–120. DOI: 10.1007/s001610100043. http://www.springerlink.com/content/cujxqmxyn3vpv4cc/
Faria, S.H.; Hutter; K. A systematic approach to the thermodynamics of single and mixed flowing media with microstructure. Part I: balance equations and jump conditions. Continuum Mech. Thermodyn. 2002, 14, 459–481. DOI:10.1007/s001610200084

2. Faria, S.H. Mechanics and Thermodynamics of Mixtures with Continuous Diversity: From Complex Media to Ice Sheets. Technische Universität Darmstadt, 2003. PDF format, 4.6 MB. Last access 11 April 2008. http://elib.tu-darmstadt.de/diss/000307/

The papers by S.H. Faria are relevant because they make mathematically clear and precise the idea of a "continuously variable similarity" between substances, which is, ashamingly, almost never made clear in the literature discussing the Gibbs paradox. Comments by Dr. P. G. L. Porta Mana, 10 April 2008

Links

Special Issue: Gibbs Paradox for the Open Access journal Entropy.
Special Issue: Symmetry and Entropy for the Open Access journal Entropy.
Special Issue: Configurational Entropy for the Open Access journal Entropy.
Papers on Configurational Entropy
Search http://xxx.lanl.gov
Entropy (ISSN 1099-4300)

Compiled by Shu-Kun Lin. Last change: 7 November 2009