A history of thermodynamics: The doctrine of energy and entropy

A History of Thermodynamics: The Doctrine of Energy and Entropy

Volumn , Issue , 2007, Pages 1-330

  Müller, Ingo ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84885781093     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-46227-9     Document Type: Book

References (398)

1. Galen: "Daß die Vermögen der Seele eine Folge der Mischungen des Körpers sind." [That the faculties of the soul follow from the composition of the body] Abhandlungen zur Geschichte der Medizin und Naturwissenschaften. Heft 21. Kraus Reprint Liechtenstein (1977).
2. W.E. Knowles Middleton: "The History of the Thermometer and its Use in Meteorology". The Johns Hopkins Press, Baltimore, Maryland (1966). Hasler table of body temperatures, cf. Fig.1.1, is the frontispiece of that book.
3. Ya.A. Smorodinsky: "Temperature". MIR Publishers, Moscow (1984).
4. "Le Opere di Galileo Galilei", Vol. XII, Firenze, Tipografia di G. Barbera (1902) p.139. The letter, and other letters by Sagredo to Galilei are replete with flattering, even sycophantic remarks which the older man seems to have appreciated. Part of that may be attributed, perhaps, to the etiquette of the time. But, in fact, it may generally be observed-even in our time-that, the more eminent a scientist already is, the more he demands praise; and a diplomat knows that.
5. Temperature measurements at extremely low temperatures are still a problem. The interested reader is referred to the publication "Die SI-Basiseinheiten. Definition, Entwicklung, Realisierung." [The SI basic units. Definition, development and realization] Physikalisch Technische Bundesanstalt, Braunschweig & Berlin (1997) p. 31-35.
6. Francis Bacon: "Novum Organum" (1620).
7. A.L. Lavoisier: "Elementary Treatise on Chemistry" (1789).
8. I. Asimov: "Biographical Encyclopedia of Science and Technology".-Pan Reference Books, London (1975).
9. Kenneth Roberts: "Oliver Wiswell." Fawcett Publications, Greenwich, Connecticut. (1940).
10. According to Varick Vanardy: "Gen. Benjamin Thompson, Count Rumford: Tinker, Tailer, Soldier, Spy." http://www.rumford.com.
11. A variant of that soup was handed out in German prisons until well into the 20th century. It was then known as "Rumfutsch". According to Ernst von Salomon: "Der Fagebogen" [The Questionaire] Rowohlt Verlag Hamburg (1951).
12. Rumford: "An inquiry concerning the source of the heat which is excited by friction". Philosophical Transactions. Vol. XVIII, p. 286.
13. J.P. Joule: "On the mechanical equivalent of heat". Philosophical Transaction. (1850) p. 61ff.
14. This observation is also mentioned by J.P. Joule: "On the mechanical equivalent of heat". Philosophical Transaction (1850) p. 61ff.
15. Later, in 1848, Mayer was involved in a political squabble and he was ridiculed publicly as having travelled as far as East India without setting his foot on land. This, however, seems to be untrue, if Mayer's diary is to be believed. He did leave the ship for a short excursion; cf. H. Schmolz, H. Weckbach: "Robert Mayer, sein Leben und Werk in Dokumenten". Veröffentlichungen des Archivs der Stadt Heilbronn. Bd. 12. Verlag H. Konrad (1964) p. 86.
16. The manuscript did survive and, when Mayer's work was eventually recognized, the paper was published in journals and books on the history of science, e.g. P. Buck (ed): "Robert Mayer-Dokumente zur Begriffsbildung des Mechanischen Äquivalents der Wärme". [Robert Mayer-documents on the emergence of concepts concerning the mechanical equivalent of heat] Reprinta historica didactica. Verlag B. Franzbecker, Bad Salzdetfurth (1980) Bd. 1, p. 20-26.
17. H. Schmolz, H. Weckbach: "Robert Mayer⋯" loc.cit p. 66, p. 78.
18. Reported by Mayer in a letter to his friend W. Griesinger on June 14th 1844. Mayer's correspondence with some of his friends is included in the collection of his works. Reprinta historica didactica. loc cit. Bd. 1, p. 121.
19. "Augsburger Allgemeine Zeitung" from May 21st, 1849.
20. [Remarks on the mechanical equivalent of heat] Verlag von Johann Ulrich Landherr, Heilbronn (1851) Bd. 1, p. 169.
21. So Mayer in an autobiographical note. Reprinta historica didactica. loc. cit. Bd. 1, p. 8.
22. J.P. Joule: "On the heating effects of magneto-electricity and on the mechanical value of heat." Philosophical Magazine, Series III, Vol. 23 (1843) p. 263ff, 347ff, 435ff.
23. J.P. Joule: Philosophical Magazine, Series III, Vol. 26 (1845), p. 369ff.
24. J.P. Joule: "On the existence of an equivalence relation between heat and the ordinary forms of mechanical power". Letter to the editors of the Philosophical Magazine and Journal. Philosophical Magazine. Series III, Vol. 27 (1845), p. 205ff.
25. J.P. Joule: "Temperature changes by expansion and compression of air." Philosophical Magazine Series III, 26 (1845) p. 369ff.
26. I. Asimov: "Biographies⋯." loc. cit.
27. Post Scriptum to Joule's memoir of 1843. loc. cit.
28. I. Asimov: "Biographies" loc. cit. The lecture was given on April, 28th 1847 in the St. Ann's Church Reading-Room in Manchester. It was published by the Manchester Courier on May 5th and May 12th.
29. J.P. Joule: "Heating during the electrolysis of water." Memoirs of the literary and Philosophical Society of Manchester. Series II, Vol. 7 (1864) p. 67.
30. H. Helmholtz: "Über die Erhaltung der Kraft" [On the conservation of force] Wissenschaftliche Abhandlungen, Bd. I (1882).
31. According to C. Kirsten, K. Zeisler (eds.): "Dokumente der Wissenschaftsgeschichte" [Documents of the history of science] Akademie Verlag, Berlin (1982) p. 6.
32. P. Lenard: "Große Naturforscher". J.F. Lehmann Verlag München (1941).
33. H. Helmholtz: "Wissenschaftliche Abhandlungen." Vol. I (1882), Vol. II (1883), Vol III (1895).
34. I. Asimov: "The rigid vacuum" in "Asimov on physics" Avon Books, New York (1976).
35. Retranslated by myself from Giulio Peruzzi: "Maxwell, der Begründer der Elektrodynamik" [Maxwell. The founder of electrodynamics] Spektrum der Wissenschaften, German edition of Scientific American. Biografie 2 (2000).
36. J.C. Maxwell: "On Faraday's lines of force." Transactions of the Cambridge Philosophical Society, X (1856).
37. J.C. Maxwell: "On physical lines of force" Parts I and II, Philosophical Magazine XXI (1861), parts III and IV, Philosophical Magazine (1862).
38. J.C. Maxwell: "A dynamical theory of the electro-magnetic field" Royal Society Transactions CLV (1864).
39. J.C. Maxwell: "Treatise on electricity and magnetism" (1873).
40. J.C. Maxwell: "An elementary treatise on electricity" William Garnett (ed.) (1881).
41. G. Mie: "Grundlagen einer Theorie der Materie" [Foundations of a theory of matter] Annalen der Physik 37, pp. 511-534; 39, pp. 1-40; 40, pp. 1-66 (1912).
42. H. Weyl: "Raum-Zeit-Materie" [Space-time-matter] Springer, Heidelberg (1921) English translation: Dover Publications, New York (1950).
43. For the integral form of these equations of balance the reader might consult I. Müller: "Thermodynamics" Pitman, Boston, London (1985) Chap. 9.
44. Another instructive account of Mie's and Weyl's treatment of electrodynamics and relativity may be found in the memoir by C.A. Truesdell and R. Toupin: "The classical field theories" Handbuch der Physik III/1 Springer. Heidelberg (1960). pp. 660-700 and 736-744.
45. A. Einstein: "Zur Elektrodynamik bewegter Körper" [On the electrodynamics of moving bodies] Annalen der Physik 17 (1905)
46. Translation of 1923 in: "The principle of relativity, a collection of original memoirs of the special and general relativity" W. Perrett, G.B. Jeffrey (eds.) Dover Publications. Introductory remarks.
47. A. Einstein: "Zur Elektrodynamik ⋯" loc. cit.
48. The actual details of Michelson's measurement are ingenious and cumbersome, because it is not easy to measure At. For details the reader may consult Michelson's papers which, incidentally, earned him the Nobel prize of physics in 1907. A.A. Michelson: "The relative motion of the earth and the luminiferous ether." American Journal of Science 22 (1881), p. 122.
49. A.A. Michelson, E.W. Morley: "Influence of motion of the medium on the velocity of light" American Journal of Science 31 (1886), p. 377.
50. H.A. Lorentz: "Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern" [Attempt of a theory of electrical and optical phenomena in moving bodies.] Leiden 1895 §§89-92.
51. Translation of 1923 in: "The principle of relativity,⋯" under the title "Michelson's interference experiment" Dover Publications. loc. cit. Lorentz acknowledges FitzGerald's priority grudgingly by saying: As FitzGerald kindly tells me, he has for a long time dealt with his hypothesis in his lectures. The then hypothetical phenomenon became known as the FitzGerald contraction, but is more often called the Lorentz contraction.
52. A. Einstein: "Zur Elektrodynamik⋯" loc. cit.
53. H.A. Lorentz: "Electro-magnetic phenomena in a system moving with any velocity less than light." English version of Proceedings of the Academy of Sciences of Amsterdam, 6 (1904).
54. Reprinted in: "The principle of relativity, ⋯" Dover Publications. loc. cit.
55. A. Einstein: "Die Grundlage der allgemeinen Relativitä tstheorie" Annalen der Physik 49 (1916).
56. English translation: "The foundation of the general theory of relativity" in: "The principle of relativity, ⋯" Dover Publications. loc. cit.
57. A. Einstein: "Zur Elektrodynamik⋯" loc. cit.
58. The notions of transverse and longitudinal mass had already been introduced by Lorentz in his paper: "Electro-magnetic phenomena ⋯" (1904) loc. cit. which Einstein later said he had been unaware of, see above.
59. In A. Einstein: "The principle of relativity,⋯" Dover Publications. loc. cit.
60. A. Einstein: "Die Grundlagen der allgemeinen Relativitä tstheorie" [On the foundation of the general theory of relativity] Annalen der Physik 49, (1916).
61. A. Einstein: "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes" [On the influence of gravitation on the properties of light]. Annalen der Physik 35, (1911).
62. Herbert George Wells (1866-1946) was a scientific visionary and social prophet, best known for his classic short story: "The time machine" first published in 1895.
63. According to I. Asimov: "The finger of God." In: "The sun shines bright." Avon Books (1981).
64. According to I. Asimov: "Biographies ⋯" loc. cit. p. 614.
65. We shall not enter into speculations about whether and how Hero of Alexandria-in the first century A.D.-employed steam power in the automatic working of doors and statues, which priests used to impose on gullible worshippers, cf. I. Asimov: "Biographies⋯" loc. cit. p. 38.
66. According to I. Asimov: "Biographies⋯" loc. cit. p. 204.
67. Yet the machines were successful. By 1775 sixty of them had been erected in Cornwall alone and there were about one hundred in the Tyne basin. According to R.J. Law: "The Steam Engine". A Science Museum booklet. Her Majesty's Stationary Office, London (1965) p. 10.
68. R.J. Law: "The Steam Engine" loc. cit. p. 13.
69. I. Asimov: "Biographies⋯" loc. cit. p. 187.
70. S. Carnot: [Reflections on the motive power of fire and on machines fitted to develop that power] à Paris chez Bachelier, Libraire. Quai des Augustin, No. 55 (1824).
71. English translation by R.H. Thurston: "Reflections on the motive power of fire by Sadi Carnot and other papers on the second low of thermodynamics by É. Clapeyron and R. Clausius." E. Mendoza (ed.) Dover Publ. New York (1960). pp. 1-59.
72. S. Carnot: "Réflexions⋯" loc. cit. p. 35.
73. S. Carnot: "Réflexions⋯" loc. cit. p. 28.
74. S. Carnot: "Réflexions⋯" loc. cit. p. 72.
75. E. Mendoza: Footnote to Carnot's "Reflections": Dover (1960) loc.cit p. 46.
76. E. Mendoza (ed.): Appendix to Carnot's "Reflections": Selection from the posthumous manuscripts of Carnot: Dover (1960) loc. cit. p. 60.
77. E. Mendoza: Introduction to Carnot's "Reflections" Dover loc. cit. p. ix.
78. E. Clapeyron: "Mémoire sur la puissance motrice de la chaleur" Journal de l'École Polytechnique. Vol XIV (1834) pp. 153-190.
79. Translations: (English) "Memoir on the motive power of heat." Scientific Memoirs Vol. 1 (1837) pp. 347-376.
80. (German) "Über die bewegende Kraft der Wärme." Annalen der Physik und Chemie Vol 135 (1843).
81. H.V. Regnault: "Relations des expériences ⋯pour déterminer les principales lois et les données numériques qui entrent dans le calcul des machines à vapeur." Mémoires de l'Académie des Sciences de línstitut de France, Paris, Vol. 21 (1847) pp. 1-748.
82. This term has been made popular by Thomas S. Kuhn in his book: "The structure of scientific revolutions." The University of Chicago Press, Chicago and London. Third edition (1996).
83. W. Thomson: "On the absolute thermometric scale founded on Carnot's theory of the motive power of heat, and calculated from Regnault's observations." Philosophical Magazine, Vol. 33 (1848) pp. 313-317.
84. W. Thomson: "An account of Carnot's theory of the motive power of heat." Transactions of the Royal Society of Edinburgh 16 (1849). pp. 5412-574.
85. R. Clausius: "Über die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärme selbst ableiten lassen." Annalen der Physik und Chemie 155 (1850). pp. 368-397.
86. Translation by W.F. Magie: "On the motive power of heat, and on the laws which can be deduced from it for the theory of heat." Dover (1960). loc. cit. pp. 109-152.
87. C. Truesdell: "The tragicomical History of Thermodynamics 1822-1854". Springer Verlag New York (1980) [The specific heat is the heat capacity per mass.].
88. R. Clausius: "Über eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie". Annalen der Physik und Chemie 169 (1854).
89. English translation: "On a modified form of the second fundamental theorem in the mechanical theory of heat." Philosophical Magazine (4) 12, (1856).
90. It was Kelvin who, in 1851, has proposed the name energy for U: W. Thomson: "On the dynamical theory of heat, with numerical results deduced from Mr. Joule's equivalent of a thermal unit, and M. Regnault's observations on steam." Transactions of the Royal Society of Edinburgh 20 (1851). p. 475. Clausius concurred: ⋯ in the sequel I shall call U the energy. It is quite surprising that Clausius let himself be preceded by Kelvin in this matter, because Clausius himself was an inveterate name-fixer. He invented the virial for something or other in his theory of real gases, see Chap. 6, and he proposed the ergal as a word for the potential energy, which seemed too long for his taste. And, of course, he invented the word entropy, see below.
91. W. Thomson, J.P. Joule: "On the thermal effects of fluids in motion." Philosophical Transactions of the Royal Society of London 143 (1853).
92. R. Clausius: "Über verschiedene für die Anwendungen bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie". Poggendorff's Annalen der Physik 125 (1865).
93. English translation by R.B. Lindsay: "On different forms of the fundamental equations of the mechanical theory of heat and their convenience for application". In: "The Second Law of Thermodynamics." J. Kestin (ed.), Stroudsburgh (Pa), Dowden Hutchinson and Ross (1976).
94. Stephen G. Brush: "Kinetic Theory" Vol I. Pergamon Press, Oxford (1965).
95. E.g. see R. Clausius: "Die mechanische Wärmetheorie" [The mechanical theory of heat] (3.ed.) Vieweg Verlag, Braunschweig (1887) p. 34.
96. I. Asimov: "Biographies" loc. cit. p. 364.
97. J. Loschmidt: "Über den Zustand des Wärmegleichgewichts eines Systems von Körpern mit Rücksicht auf die Schwerkraft." [On the state of the equilibrium of heat of a system of bodies in regard to gravitation.] Sitzungsberichte der Akademie der Wissenschaften in Wien, Abteilung 2, 73: pp. 128-142, 366-372 (1876), 75: pp. 287-298, (1877), 76: pp. 205-209, (1878).
98. O. Spengler: "Der Untergang des Abendlandes: Kapitel VI. Faustische und Apollinische Naturerkenntnis. § 14: Die Entropie und der Mythos der Götterdämmerung." Beck'sche Verlagsbuchhandlung. München (1919) pp. 601-607.
99. According to S.G. Brush: "The Temperature of History. Phases of Science and Culture in the Nineteenth century." Burt Franklin & Co. New York (1978).
100. N. Georgescu-Roegen: "The Entropy Law and the Economic Process." Harvard University Press, Cambridge, Mass (1971).
101. I. Müller, W. Weiss: "Entropy and Energy-A Universal Competition, Chap. 20: Socio-thermodynamics." Springer, Heidelberg, (2005). A simplified version of socio-thermodynamics is presented at the end of Chap. 5.
102. G. Jaumann: "Geschlossenes System physikalischer und chemischer Differentialgesetze" [Closed system of physical and chemical differential laws] Sitzungsbericht Akademie der Wissenschaften Wien, 12 (IIa) (1911).
103. E. Lohr: "Entropie und geschlossenes Gleichungssystem" [Entropy and closed system] Denkschrift der Akademie der Wissenschaften, 93 (1926).
104. K.R. Popper: "Objective knowledge-an evolutionary approach." Clarendon Press, Oxford (1972).
105. D. Bernoulli: "Hydrodynamica, sive de vivibus et motibus fluidorum commentarii. Sectio decima: De affectionibus atque motibus fluidorum elasticorum, praecique autem aëris".
106. English translation of Sect. 10: "On the properties and motions of elastic fluids, particularly air". In S. Brush: "Kinetic theory" Vol I, Pergamon Press, Oxford (1965).
107. According to D. Lindley: "Boltzmann's atom". The Free Press, New York (2001), p. 1.
108. S.G. Brush reviews, at some length, the efforts of both scientist to publish their works in his comprehensive memoir: "The kind of motion we call heat, a history of the kinetic theory of gases in the 19th century" Vol I pp. 107-159. North Holland Publishing Company, Amsterdam (1976). Brush reports that Lord Rayleigh found Waterston's paper in the archives of the Royal Society, and published it in 1893, 48 years after it was submitted. Rayleigh added an introduction in which he gave good advise for junior scientists by saying that ⋯. highly speculative investigations, especially by an unknown author, are best brought before the world through some other channel than a scientific society. Rayleigh praises the marvellous courage of the author, i.e. Waterston, and provides some additional council: A young author, who believes himself capable of great things, would usually do well to secure the favourable recognition of the scientific world by work whose scope is limited, and whose value is easily judged, before embarking on higher flights. I do not know whether Lord Raleigh was serious, when he wrote these sentences, or whether, perhaps, he was being sarcastic.
109. J.C. Maxwell: "On the dynamical theory of gases". Philosophical Transactions of the Royal Society of London 157 (1867).
110. R. Clausius: "Über die Art der Bewegung, welche wir Wärme nennen," Annalen der Physik 100, (1857) pp. 353-380.
111. S.G. Brush: "The kind of motion we call heat." loc. cit.
112. A.K. Krönig: "Grundzüge einer Theorie der Gase". [Basic theory of gases] Annalen der Physik 99 (1856), p. 315.
113. J.P. Joule: "Remarks on the heat and the constitution of elastic fluids". Memoirs of the Manchester Literary and Philosophical Society. November 1851.
114. Reprinted in Philosophical Magazine. Series IV, Vol. XIV (1857), p. 211.
115. R. Clausius: "Über die mittlere Länge der Wege, welche bei Molekularbewegung gasförmiger Körper von den einzelnen Molekülen zurückgelegt werden, nebst einigen anderen Bemerkungen über die mechanische Wärmetheorie". Annalen der Physik (2) 105 (1858) pp. 239-258.
116. English translation: "On the mean free path of the molecular motion in gaseous bodies; also other remarks on the mechanical theory of heat." In S. Brush: "Kinetic theory." Vol I, Pergamon Press, Oxford (1965).
117. J. Loschmidt: Zur Grösse der Luftmolecüle. [On the size of air molecules] Zeitschrift für mathematische Physik 10, (1865), p. 511.
118. Giulio Peruzzi: "Maxwell, der Begründer der Elektrodynamik" [Maxwell the founder of electrodynamics] Spektrum der Wissenschaften, German edition of Scientific American. Biografie 2 (2000).
119. Maxwell wrote several papers on the kinetic theory. Here we are concerned with the first one: J.C. Maxwell: "Illustrations of the dynamical theory of gases." Philosophical Magazine 19 and 20, both (1860).
120. J.C. Maxwell: "On theories of the constitution of Saturn's rings." Proceedings of the Royal Society of Edinburgh IV (1859).
121. J.C. Maxwell: "On the Stability of the Motion of Saturn's Rings." An Essay which obtained the Adams Prize for the year 1856, in the University of Cambridge.
122. A. Quételet: "La théorie des probabilités appliquées aux sciences morales et politiques".
123. J. Herschel: Edinburgh Review 92 (1850).
124. L. Boltzmann: "Der zweite Hauptsatz der mechanischen Wärmetheorie" [The second law of the mechanical theory of heat]. Lecture given at the Kaiserliche Akademie der Wissenschaften on May 29, 1886.
125. L. Boltzmann: "Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten." [Studies on the equilibrium of kinetic energy between moving material points] Wiener Berichte 58 (1868) pp. 517-560.
126. J.C. Maxwell: "On Boltzmann's theorem on the average distribution of energy in a system of material points." Cambridge Philosophical Society's Transactions XII (1879).
127. L. Boltzmann: "Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen". [Further studies about the heat equilibrium among gas molecules] Sitzungsberichte der Akademie der Wissenschaften Wien (II) 66 (1872) pp. 275-370.
128. That cumbersome word-even for German ears-describes a formula for the number of collisions which lead to a particular scattering angle by the binary interaction of atoms. The expression is not due to Maxwell, of course, nor to Boltzmann. As far as I can find out it was first used by P. and T. Ehrenfest in "Conceptual Foundations of the Statistical Approach in Mechanics." Reprinted: Cornell University Press, Ithaca (1959). The word seems to be untranslatable, and so it has been joined to the small lexicon of German words in the English language like Kindergarten, Zeitgeist, Realpolitik and, indeed, Ansatz.
129. All this is terribly anachronistic but it belongs here. Grad proposed the moment approximation of the distribution function in 1949! H. Grad: "On the kinetic theory of rarefied gases." Communications of Pure and Applied Mathematics 2 (1949).
130. L. Boltzmann: "Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht". [On the relation between the second law of the mechanical theory of heat and probability calculus, or the theories on the equilibrium of heat.] Sitzungsberichte der Wiener Akademie, Band 76, 11. Oktober 1877.
131. L. Boltzmann: "Vorlesungen über Gastheorie I und II". [Lectures on gas theory] Verlag Metzger und Wittig, Leipzig (1895) and (1898).
132. L. Boltzmann: "Der zweite Hauptsatz der mechanischen Wärmetheorie". [The second law of the mechanical theory of heat] Lecture given at a ceremony of the Kaiserliche Akademie der Wissenschaften on May, 29th, 1886.
133. See also: E. Broda: "Ludwig Boltzmann. Populäre Schriften". Verlag Vieweg Braunschweig (1979) p. 26.
134. L. Boltzmann: "Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatz der Wärmetheorie". [On the relation of a general mechanical theorem and the second law of thermodynamics] Sitzungsberichte der Akademie der Wissenschaften Wien (II) 75 (1877).
135. W. Thomson: "The kinetic theory of energy dissipation" Proceedings of the Royal Society of Edinburgh 8 (1874) pp. 325-334.
136. J.W. Gibbs: "On the equilibrium of heterogeneous substances." Transactions of the Connecticut Academy 3 (1876) p. 229.
137. Later Zermelo even helped to make statistical mechanics known among physicists by editing a German translation of Gibbs's "Elementary principles of statistical mechanics", see below.
138. H. Poincaré: "Sur le problème des trois corps et les équations de dynamique" [On the three-body problem and the dynamical equations] Acta mathematica 13 (1890) pp.1-270.
139. See also: H. Poincaré: "Le mécanisme et l'expérience" [Mechanics and experience] Revue Métaphysique Morale 1 (1893) pp. 534-537.
140. E. Zermelo: "Über einen Satz der Dynamik und die mechanische Wärmelehre" [On a theorem of dynamics and the mechanical theory of heat] Annalen der Physik 57 (1896) pp. 485-494.
141. L. Boltzmann: "Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E. Zermelo" [Reply to the considerations of Mr. E. Zermelo on the theory of heat] Annalen der Physik 57 (1896) pp. 773-784.
142. E. Zermelo: "Über mechanische Erklärungen irreversibler Vorgänge. Eine Antwort auf Hrn. Boltzmanns "Entgegnung". ["On mechanical explanations of irreversible processes. A response to Mr. Boltzmann's "reply"] Annalen der Physik 59 (1896), pp. 392-398.
143. L. Boltzmann: "Zu Hrn. Zermelos Abhandlung "Über die mechanische Erklärung irreversibler Vorgänge" [On Mr. Zermelo's treatise "On the mechanical explanation of irreversible processes"] Annalen der Physik 59 (1896) pp. 793-801.
144. L. Boltzmann: "Über die statistische Mechanik" [On statistical mechanics] Lecture given at a scientific meeting in connection with the World Fair in St. Louis (1904). See also: E. Broda (1979) loc. cit. pp. 206-224.
145. According to G. Peruzzi (2000) loc. cit. p. 93 f. the demon was first conceived in a letter by Tait to Maxwell in (1867). It appeared in print in Maxwell's "Theory of Heat" Longmans, Green & Co. London (1871).
146. M.J. Klein: American Science 58 (1970).
147. I recommend an excellent account of Boltzmann's professional work and psyche by D. Lindley: "Boltzmann's atom." The Free Press, New York, London (2001). Lindley starts his Introduction with the apodictic quotation from Mach: "I don't believe that atoms exist."
148. L. Boltzmann: "Eine Antrittsvorlesung zur Naturphilosophie" [Inaugural lecture on natural philosophy] Reprinted in the journal "Zeit" December 11, 1903 See also: E. Broda: loc. cit.
149. L. Boltzmann: "Über eine These von Schopenhauer" Lecture to the Philosophical Society of Vienna, given on January 21, 1905. See also: E. Broda: loc. cit.
150. L. Boltzmann: "Über die Frage nach der objektiven Existenz der Vorgänge in der unbelebten Natur" [On the question of the objective existence of events in the inanimate nature] Sitzungsberichte der kaiserlichen Akademie der Wissenschaften in Wien. Mathematisch-naturwissenschaftliche Klasse; Bd. CVI. Abt. II (1897) p. 83ff.
151. Boltzmann does not seem to have argued like that. I read about this idea in one of Asimov's scientific essays. I. Asimov: "The modern demonology" in "Asimov on Physics." Avon Publishers of Bard, New York (1979).
152. K.H. Meyer & C. Ferri: "Sur l'élasticité du caoutchouc". Helvetica Chimica Acta 29, p. 570 (1935).
153. I. Müller, W. Weiss: "Entropy and energy-a universal competition" Springer, Heidelberg (2005). In Chap. 5 of that book the analogy between thermodynamic properties of rubber and gases is highlighted by a juxtaposition.
154. W. Kuhn: "Über die Gestalt fadenförmiger Moleküle in Lösungen" [On the shape of filiform molecules in solution] Kolloidzeitschrift 68, p. 2 (1934).
155. W. Kuhn: "Beziehungen zwischen Molekülgröße, statistischer Molekülgestalt und elastischen Eigenschaften hochpolymerer Stoffe" [Relations between molecular size, statistical molecular shape and elastic properties of high polymers] Kolloidzeitschrift 76, p. 258 (1936).
156. Modern representations of the field may be found in the monograph by P.J. Flory: "Principles of Polymer Chemistry." Cornell University Press, Ithaca (1953). The book has gone through many editions and re-printings in later years.
157. For a discussion of rubber elasticity in some detail and a discussion of the limitations of the Kinetic Theory of Rubber the reader is referred to the booklet "Rubber and Rubber Balloons-Paradigms of Thermodynamics" by I. Müller and P. Strehlow, Springer Lecture Notes in Physics, Springer, Heidelberg (2005).
158. J.W. Gibbs: "Elementary principles in statistical mechanics-developed with especial reference to the rational foundation of thermodynamics." Yale University Press (1902). This memoir is available as a Dover booklet, first published in 1960. My page numbers refer to the Dover publication.
159. J.E. Mayer, M.G. Mayer: "Statistical Mechanics." John Wiley & Sons, New York (1940) Chap. 13.
160. O. Kastner: "Zweidimensionale molekular-dynamische Untersuchung des Austenit <-> Martensit Phasenübergangs in Formgedä chtnislegierungen." [Two-dimensional molecular dynamics of the austenite <-> martensite phase transition in shape memory alloys] Dissertation TU Berlin, Shaker Verlag (2003).
161. E. Schrödinger: "Statistical thermodynamics. A course of seminar lectures." Cambridge at the University Press (1948).
162. I found this simple problem in the book by J.D. Fast: "Entropie. Die Bedeutung des Entropiebegriffs und seine Anwendung in Wissenschaft und Technik." [Entropy. The meaning of the concept of entropy and its application in science and technology] Philips's Technische Bibliothek (1960). Also available in Dutch, English, French, and Spanish.
163. C.E. Shannon: "A mathematical theory of communication." Bell Systems Technology Journal 27, (1948), pp. 379-423, 623-657.
164. K. Denbigh: "How subjective is entropy?". In: "Maxwell's demon, entropy, information, computing." H.S. Leff, A.F. Rex (eds.) Rrinceton University Press (1990) pp. 109-115.
165. I. Asimov: "Biographies ⋯" loc. cit.
166. So Ostwald in the foreword of his translation: "Thermodynamische Studien von J. Willard Gibbs" [Thermodynamic studies by J. Willard Gibbs] Verlag W. Engelmann, Leipzig (1892).
167. A. Sommerfeld: "Vorlesungen über theoretische Physik, Bd. V, Thermodynamik und Statistik" [Lectures on theoretical physics, Vol. V. Thermodynamics and Statistics] Dietrich'sche Verlagsbuchhandlung, Wiesbaden, 1952 p. 76.
168. I. Asimov: "Biographies⋯." loc.cit p. 441.
169. These and other examples have been worked out by Müller and Weiss in a recent book. I. Müller, W. Weiss: "Entropy and energy-a universal competition." Springer, Heidelberg (2005).
170. Berthollet was yet another scientist ennobled and made a senator by Napoléon, who generally knew how to create loyal followers. In the case of Berthollet, however, he made a mistake, because the chemist later voted for the deposition of the emperor. That gained him a peerage under the returning Bourbons, cf. I. Asimov: "Biographies⋯." loc. cit.
171. C.L. Berthollet: "Essay de statique chimique" (1803).
172. H. Helmholtz; "Die Thermodynamik chemischer Vorgänge" [Thermodynamics of chemical processes] Sitzungsberichte der preussischen Akademie der Wissenschaften. Berlin (1882).
173. It is a sign of the schizophrenia of German politics between the two world wars that the Kaiser Wilhelm Institute retained its name in the time of the Weimar republic and during the national-socialist rule, although the monarchy was thoroughly discredited. It took another world war to shake the name loose. The institute was renamed Max Planck Institute in 1946, cf. M. Planck: "Physikalische Abhandlungen und Vortraege" [Papers and lectures on physics] Vieweg, Braunschweig (1958). Foreword by M.von Laue.
174. According to I. Asimov: "Biographies." loc.cit
175. According to A. Galland: "Die Ersten und die Letzten, die Jagdflieger im Zweiten Weltkrieg." [The first and the last, fighter pilots in World War II] Verlag Schneekluth, Augsburg (1953). Adolf Galland was himself a highly decorated fighter pilot before he was given an office job; he became the last inspector of the Luftwaffe in the war and then the first inspector of the after-war Luftwaffe in 1956.
176. J. Maynard-Smith, G.R. Price: "The logic of animal conflict." Nature 246 (1973).
177. P.D. Straffin: "Game Theory and Strategy." New Mathematical Library. The Mathematical Association of America 36 (1993).
178. I. Müller: Continuum Mechanics and Thermodynamics 14 (2002) pp. 389-404.
179. The simplified presentation given above follows a paper by J. Kalisch, I. Müller: "Strategic and evolutionary equilibria in a population of hawks and doves." Rendiconti del Circolo Matematico in Palermo, Serie II, Supplemento 78 (2006), pp. 163-171. That paper also includes evolutionary processes, which make the hawk fraction change so that the population may eventually reach the evolutionarily stable strategy appropriate to the price level T.
180. J. Mimkes: "Binary alloys as a model for a multicultural society." Journal of Thermal Analysis 43 (1995).
181. W. Nernst: "Über die Berechnung chemischer Gleichgewichte aus thermodynamischen Messungen" [On calculations of chemical equilibria from thermodynamic measurements] Königliche Gesellschaft der Wissenschaften Göttingen 1, (1906).
182. W. Nernst: "Thermodynamik und spezifische Wärme" [Thermodynamics and specific heat]. Berichte der königlichen preußischen Akademie der Wissenschaften (1912).
183. W. Nernst: "Die theoretischen und experimentellen Grundlagen des neuen Wärmesatzes." [Theoretical and experimental basis for the new heat theorem] Verlag W. Knapp, Halle (1917), p. 77.
184. According to I. Asimov: "The unlikely twins" in: "The tragedy of the moon" Dell Publishing Co. New York (1972).
185. J. Wilks: "Der dritte Hauptsatz der Thermodynamik" [The third law of thermodynamics] Vieweg, Braunschweig (1963)
186. I. Asimov: "Biographies ⋯" loc.cit.
187. W. Nernst: "Über die Berechnung⋯." loc.cit. (1906).
188. See: A. Hermann (ed.): "Deutsche Nobelpreisträger" [German winners of the Nobel prize] Heinz Moos Verlag, München (1969) p. 131-132.
189. J.D. van der Waals: "Over de continuiteit van den gasen vloeistoftoestand." [On the continuity of the gaseous and the liquid state]. Dissertation, Leiden (1873).
190. In: Encyclopadie der mathematischen Wissenschaften, Bd. V.1. p. 550.
191. M.M. Abbott: Chemical Engineering Progress, February (1989).
192. I. Müller, W. Weiss: "Entropy and energy,⋯" loc.cit. (2001).
193. I. Müller, P. Villaggio: "A model for an elastic-plastic body" Archive for Rational Mechanics and Analysis. 65 (1977).
194. L. Tisza: "Transport phenomena in He II." Nature 141 (1938).
195. L.D. Landau: "The theory of superfluidity of Helium II." Journal of Physics (USSR) 5 (1941).
196. E.M. Lifshitz: "Radiation of sound in Helium II." Journal of Physics (USSR) 8 (1944).
197. D.V. Osborne: "The rotation of liquid Helium II" Proceedings Physical Society A 63 (1950).
198. The photograph is taken from an article by P. Strehlow: "Die Kapitulation der Entropie-100 Jahre III. Hauptsatz der Thermodynamik." [The capitulation of entropy-100 years of 3rd law of thermodynamics] Physik Journal 4 (12) 2005.
199. The idea of having an occupancy of an arbitrary number d was introduced by G. Gentile: "Osservazioni sopra le statistiche intermedie." [Observations on intermediate statistics] Nuovo Cimento 17, p. 493-497.
200. S.N. Bose: "Planck's Gesetz und Lichtquantenhypothese." [Planck's law and the hypothesis of light quanta] Zeitschrift für Physik 26 (1924).
201. A. Einstein: "Quantentheorie des einatomigen idealen Gases." [Quantum theory of a monatomic ideal gas] Sitzungsberichte physikalisch mathematische Klasse, September 1924 pp. 261-267.
202. A. Einstein: "Quantentheorie des einatomigen idealen Gases II" [Quantum theory of a monatomic ideal gas. II] Sitzungsberichte physikalisch mathematische Klasse, February 1925 pp. 3-14.
203. E. Schrödinger: "Statistical thermodynamics." Cambridge at the University Press (1948).
204. M. Dutta: "Satyendra Nath Bose-life and work." Journal of Physics Education. 2 (1975).
205. Actually Fermi's article appeared in: E. Fermi: Zeitschrift für Physik 86 (1926) p. 902.
206. Diracs contribution may be found in: P.A.M. Dirac: Proceedings of the Royal Society (A) 41 (1927) p. 24.
207. I. Asimov: "Biographies⋯" loc.cit. p. 377.
208. W. Wien: Wiedemann's Annalen 58 (1896) p. 662.
209. M. Planck: "Über elektrische Schwingungen, welche durch Resonanz erregt und durch Strahlung gedämpft werden." [On electrical oscillations excited by resonance and damped by radiation] Sitzungsberichte der königlichen Akademie der Wissenschaften in Berlin, mathematisch- physikalische Klasse, 21.3.1895. Wiedemann's Annalen 57 (1896) p. 1. Planck was much interested in radiation; primarily because he believed for a long time that radiation damping is the essential mechanism of irreversibility. Boltzmann opposed the idea and eventually Planck disabused himself of it.
210. This equation and the following argument are too complex to be derived here, even as an Insert. However, they are replayed in all good books on electrodynamics. I found a particularly clear presentation in R. Becker, F. Sauter: "Theorie der Elektrizität." [Theory of electricity.] Vol. 2 Teubner Verlag, Stuttgart (1959).
211. Lord Rayleigh: Philosophical Magazine 49 (1900) p. 539.
212. So named by Paul Ehrenfest in 1910,-posthumously says S.G. Brush: "The kind of motion we call heat ⋯" loc. cit. p. 306. And indeed, by that time, to all intents and purposes, the Raleigh-Jeans theory was dead.
213. [On the theory of the law of energy distribution in the normal spectrum] M. Planck: Verhandlungen der deutschen physikalischen Gesellschaft 2 (1900) p. 202. Normal spectrum is Planck's word for the black body spectrum.
214. There were three such papers. Apart from the one cited above they are M. Planck: "Über eine Verbesserung der Wien'schen Spektralgleichung. " [On an improvement of Wien's spectral equation] Verhandlungen der deutschen physikalischen Gesellschaft 2 (1900) pp. 202-204.
215. M. Planck: "Über das Gesetz der Energieverteilung im Normalspektrum." [On the law of energy distribution in the normal spectrum.] Annalen der Physik (4) 4 (1901) pp. 553-563.
216. These researches were published in 1901: H. Rubens, F. Kurlbaum: Annalen der Physik 4 (1901) p. 649.
217. O. Lummer, E. Pringsheim: Annalen der Physik 6 (1901) p. 210.
218. M. Planck: "Die Entstehung und bisherige Entwicklung der Quantentheorie." [The origin and subsequent development of quantum theory] Nobel lecture to the Royal Swedish Academy of Sciences in Stockholm, held on June 2nd, 1920.
219. P.A. Schilpp (ed.): "Albert Einstein: Philosopher-Scientist." Library of living philosophers, New York (1949).
220. J.H. Jeans. Philosophical Magazine, February 1909 p. 229. J.H. Jeans: Ibidem, July 1909 p. 209
221. M. Planck: "Zur Theorie der Wärmestrahlung." [On the theory of heat radiation] Annalen der Physik (4) 31 (1910) pp. 758-768.
222. P.A. Schilpp (ed.): In: "Albert Einstein: Philosopher-Scientist. " "Autobiographical notes." loc. cit.
223. According to I. Asimov: "Biographies" loc. cit. p. 506.
224. M. Planck: "Eine neue Strahlungshypothese." [A new hypothesis about radiation] Verhandlungen der deutschen physikalischen Gesellschaft, February 3, 1911.
225. M. Planck: "Über den zweiten Hauptsatz der mechanischen Wärmetheorie." [On the second law of the mechanical theory of heat] Dissertation, Universität München (1879).
226. D. Lindley: "Boltzmann's atom." loc.cit. p. 212.
227. A. Hermann (ed.): "Deutsche Nobelpreisträger" loc. cit. p. 91.
228. This is the somewhat shortened quotation from M. Planck: "A Scientific autobiography and other papers." Williams and Norgate, London (1950). Brush writes: I suppose that most people who read (or repeat) this quotation think Planck is referring to his quantum theory, but in fact he was talking about his struggle to convince scientists in the 1880's and 1890's that the second law of thermodynamics involves a principle of irreversibility, and that the flow of energy from hot to cold is not analogous to the flow of water from a high level to a low one, as Ostwald and the energeticists claimed.
229. Cf. S.G. Brush: "The kind of motion we call heat,⋯" loc. cit. p. 640.
230. A. Einstein: "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Standpunkt." [On a heuristic point of view concerning the creation and reaction of light.] Annalen der Physik (4) 17 (1905).
231. I. Asimov: "Biographies⋯" loc.cit. p. 517.
232. A. Hermann (ed): "Deutsche Nobelpreisträger." loc.cit. p. 91.
233. Asimov: "Biographies⋯" loc.cit. p. 589.
234. A. Einstein: "Strahlungsemission und-absorption nach der Quantentheorie." Deutsche physikalische Gesellschaft, Verhandlungen 18 pp. 318-323 (1916).
235. A. Einstein: "Quantentheorie der Strahlung." Physikalische Gesellschaft Zürich, Mitteilungen 16 pp. 47-62 (1916).
236. A. Einstein: "Quantentheorie der Strahlung." [Quantum theory of radiation] Physikalische Zeitschrift 18 pp. 121-128 (1917).
237. S.N. Bose: "Plancks Gesetz⋯" loc. cit.
238. W. Weiss: "The balance of entropy on earth." Thermodynamics and Continuum Mechanics 8, (1996).
239. In his booklet: E. Schrödinger: "What is Life?" Cambridge: At the University Press. New York: The Macmillan Company (1945).
240. W. Thomson: "On the convective equilibrium of temperature in the atmosphere." Proceedings of the Literary and Philosophical Society of Manchester (3) II (1862) pp. 125-131.
241. See also: W. Thomson: Philosophical Magazine 22 (1887) p. 287
242. W. Thomson: "Mathematical and Physical Papers." 5 Cambridge (1911) p. 256.
243. J. Homer Lane: American Journal of Science and Arts. Series 2 Vol. 4 (1870) p. 57.
244. So called by S. Chandrasekhar: "An Introduction to the Study of Stellar Structure." University of Chicago Press (1939) p. 88. Reprinted by Dover Publications (1957). Page numbers refer to the Dover edition. Chandrasekhar also gives much credit to A. Ritter who investigated the condition of convective equilibrium in a star independently of Lane's work. Ritter published 18 papers "Untersuchungen über die Höhe der Atmosphäre und die Constitution gasförmiger Weltkörper." [Investigations on the height of the atmosphere and the constitution of gaseous bodies] Wiedemann Annalen (1878-1883). Those papers says Chandrasekhar ⋯form a classic the value of which has never been adequately recognized⋯and he is tempted to rename the Lane-Emden equation and call it the Lane-Ritter equation. However, Emden gave much credit to Ritter.
245. R. Emden: "Gaskugeln: Anwendungen der mechanischen Wärmetheorie." [Gas spheres: Applications of the mechanical theory of heat] Teubner, Leipzig and Berlin (1907).
246. K. Schwarzschild: "Über das Gleichgewicht der Sonnenatmosphäre." [On the equilibrium of the solar atmosphere] Göttinger Nachrichten 1906 p. 41.
247. K. Schwarzschild: "Über Diffusion und Absorption in der Sonnenatmosphäre." [On diffusion and absorption in the solar atmosphere] Berliner Sitzungsberichte 1914 p. 1183.
248. S. Rosseland: "Note on the absorption of radiation within a star." Monthly Notices Vol. 84 (1924) p. 525.
249. S. Rosseland: "The theory of the stellar absorption coefficient." Astrophysical Journal Vol. 61 (1925) p. 424.
250. A. Einstein: "Quantentheorie der Strahlung." (1917) loc.cit.
251. E.g. see: S. Rosseland: "Astrophysik auf atomtheoretischer Grundlage." [Astrophysics based on atomic theory] Springer, Berlin (1931).
252. K. Schwarzschild: Göttinger Nachrichten (1906).
253. A.S. Eddington: "The Internal Constitution of the Stars." Cambridge, University Press (1926).
254. According to I. Asimov: "Biographies ⋯" loc. cit. p.603.
255. A.S. Eddington: "The internal Constitution of the Stars." loc.cit p. 145.
256. D.I. Mendelejew: Chemisches Centralblatt (1904) Vol. I p. 137.
257. A.L. Wegener: Thermodynamik der Atmosphäre [Thermodynmics of the atmosphere] Verlag J.A. Barth, Leipzig (1911).
258. M. Fourier: "Analytische Theorie der Wärme." Translated by Dr. B. Weinstein. Springer, Berlin (1884).
259. I. Asimov: "Biographies⋯" loc.cit. p. 234.
260. W. Thomson: "On the secular cooling of the earth." Transactions of the Royal Society of Edinburgh (1862).
261. I. Asimov: "Biographies⋯" loc. cit. p. 380.
262. A. Fick: "Ueber Diffusion." [On diffusion] Annalen der Physik 94 (1855) pp. 59-86.
263. I. Asimov: "Biographies⋯" loc. cit. p. 354.
264. G.G. Stokes: "Mathematical and Physical Papers." Cambridge at the Universities Press (1880-1905).
265. G.G. Stokes: "On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids." Transactions of the Cambridge Philosophical Society. III (1845) p. 287.
266. L. Navier: Mémoires de l'Académie des Sciences VI (1822) p. 389.
267. S.D. Poisson: Journal de l'Ecole Polytechnique XIII cahier 20 p. 139.
268. G.G Stokes: "On the effect of the internal friction of fluids on the motion of pendulums." Transactions of the Cambridge Philosophical Society IX (1851) p. 8.
269. G.G. Stokes: "On the theories of the internal friction⋯. " loc.cit. p. 312.
270. C. Eckart: "The thermodynamics of irreversible processes I: The simple fluid." Physical Review 58, (1940)
271. C. Eckart: "The thermodynamics of irreversible processes II: Fluid mixtures." Physical Review 58, (1940).
272. G. Jaumann: "Geschlossenes System⋯" loc. Cit.
273. E. Lohr: "Entropie und geschlossenes Gleichungssystem," loc. cit.
274. J. Meixner: "Zur Thermodynamik der irreversiblen Prozesse in Gasen mit chemisch reagierenden, dissoziierenden and anregbaren Komponenten." [On thermodynamics of irreversible processes in gases with reacting, dissociating and excitable components] Annalen der Physik (5) 43 (1943) pp. 244-270.
275. J. Meixner: Zeitschrift der physikalischen Chemie B 53 (1943) p. 235.
276. I. Prigogine: "Étude thermodynamique des phé nomènes irréversibles." Desoer, Liège (1947).
277. S.R. de Groot, P. Mazur: "Non-Equilibrium Thermodynamics" North Holland, Amsterdam (1963).
278. C. Truesdell: "Six Lectures on Modern Natural Philosophy" Springer 1966.
279. C. Truesdell: "Rational thermodynamics." McGraw-Hill series in modern applied mathematics (1969) Chap. 7.
280. C. Eckart: "The thermodynamics of irreversible processes III: Relativistic theory of the simple fluid." Physical Review 58 (1940).
281. L. Onsager: "Reciprocal relations in irreversible processes." Physical Review (2) 37 (1931) pp. 405-426 and 38 (1932) pp. 2265-2279.
282. H.B.G. Casimir: "On Onsager's principle of microscopic reversibility." Review of Modern Physics 17 (1945) pp. 343-350.
283. J. Meixner, H.G. Reik: "Die Thermodynamik der irreversiblen Prozesse in kontinuierlichen Medien mit inneren Umwandlungen." [Thermodynamics of irreversible processes in continuous media with internal transformations] Handbuch der Physik III/2, Springer Heidelberg (1959).
284. C. Truesdell: "Mechanical Basis of diffusion." Journal of Chemical Physics 37 (1962).
285. I. Müller: "A new approach to thermodynamics of simple mixtures." Zeitschrift für Naturforschung 28a (1973).
286. J. Meixner: Annalen der Physik (1943) loc.cit.
287. H. Giesekus: "Die rheologische Zustandsgleichung." [The rheological equation of state] Rheologica Acta 1 (1958) pp. 2-20.
288. W. Noll: "A mathematical theory of the mechanical behaviour of continuous media." Archive for Rational Mechanics and Analysis 2 (1958).
289. I. Müller: "On the frame-dependence of stress and heat flux." Archive for Rational Mechanics and Analysis 45 (1972).
290. W. Noll: "A new mathematical theory of simple materials." Archive for Rational Mechanics and Analysis 48 (1972).
291. C. Truesdell: "Correction of two errors in the kinetic theory that have been used to cast unfounded doubt upon the principle of material frame indifference." Meccanica 11 (1976).
292. One of the "errors" in Truesdell's opinion was supposed to occur in Müller's argument, cf. Insert 8.1. The other one was suspected by Truesdell to be contained in a paper by D.G.B. Edelen, T.A. McLennan: "Material Indifference: A Principle or a Convenience." International Journal of Engineering Science 11 (1973).
293. B.D. Coleman: "Thermodynamics of materials with memory." Archive for Rational Mechanics and Analysis 17 (1964).
294. B.D. Coleman, W. Noll: "An approximation theorem for functionals, with applications in continuum mechanics" Archive for Rational Mechanics and Analysis 6 (1960).
295. E.g. see C. Truesdell: "The elements of continuum mechanics" Springer, New York (1966).
296. Also: B.D. Coleman, H. Markovitz, W. Noll: "Viscometric flows of non-Newtonian fluids." Springer Tract in Natural Philosophy 5 (1966).
297. J.E. Dunn, R.L. Fosdick: "Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade." Archive for Rational Mechanics and Analysis 56 (1974).
298. D.D. Joseph: "Instability of the rest state of fluids of arbitrary grade greater than one." Archive for Rational Mechanics and Analysis. 75 (1981).
299. L.C. Woods: Bulletin of Mathematics and its Applications 1 (1981).
300. In relativistic thermodynamics we require invariance of the equations under Lorentz transfomations, but this is not a subject of this book, although relativistic thermodynamics is an interesting application of extended thermodynamics. See: I-Shih Liu, I. Müller, T. Ruggeri: "Relativistic thermodynamics of gases." Annals of Physics 100 (1986).
301. Also: I. Müller, T. Ruggeri: "Rational Extended Thermodynamics." Springer, New York (1998) 2nd edition.
302. I-Shih Liu: "Method of Lagrange multipliers for the exploitation of the entropy principle." Archive for Rational Mechanics and Analysis 46 (1972).
303. An excellent review of waves-in particular acceleration waves-is given by P. Chen: "Growth and decay of waves in solids. Mechanics of Solids III" Handbuch der Physik 6A/3 Springer, Heidelberg (1973).
304. I believe that the first person to calculate the rate of change of the amplitude A(t) of an acceleration wave was W.A. Green: "The growth of plane discontinuities propagating into a homogeneous deformed material." Archive for Rational Mechanics and Analysis 16 (1964).
305. The present compact form of the Bernoulli equation-with right and left eigenvectors-is due to G. Boillat: "La propagation des ondes." Gauthier-Villars, Paris (1965).
306. S. Kawashima: "Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications." Proceedings of the Royal Society of Edinburgh A 106 (1987).
307. W. Weiss: "Zur Hierarchie der erweiterten Thermodynamik." [On the hierarchy of extended thermodynamics] Dissertation TU Berlin.
308. See also: I. Müller, T. Ruggeri: "Rational Extended Thermodynamics." loc.cit.
309. G. Boillat, T. Ruggeri: "Moment equations in the kinetic theory of gases and wave velocities." Continuum Mechanics and Thermodynamics 9 (1997).
310. G. Boillat, T. Ruggeri: "Moment equations ⋯" loc.cit.
311. C. Cattaneo: "Sulla conduzione del calore." [On heat conduction] Atti del Seminario Matematico Fisico della Università di Modena, 3 (1948).
312. The instabilities involved in the Chapman-Enskog iterative scheme have recently been reviewed by Henning Struchtrup (1956-). H. Struchtrup: "Macroscopic Transport Equations for Rarefied Gases-Approximation Methods in Kinetic Theory" Springer, Heidelberg (2005).
313. I. Müller: "Zur Ausbreitungsgeschwindigkeit von Störungen in kontinuierlichen Medien." [On the speed of propagation in continuous bodies.]. Dissertation TH Aachen (1966).
314. See also: I. Müller: "Zum Paradox der Wä rmeleitungstheorie." [On the paradox of heat conduction]. Zeitschrift für Physik 198 (1967).
315. I-Shih Liu, I. Müller: "Extended thermodynamics of classical and degenerate gases." Archive for Rational Mechanics and Analysis 46 (1983).
316. S.K. Godunov: "An interesting class of quasi-linear systems." Soviet Mathematics 2 (1961).
317. K.O. Friedrichs, P.D. Lax: "Systems of conservation equations with a convex extension." Proceeding of the National Academy of Science USA 68 (1971).
318. Boillat: "Sur l'éxistence et la recherche d'équations de conservations supplémentaires pour les systèmes hyperbolique." [On the existence and investigation of supplementary conservation laws for hyperbolic systems] Comptes Rendues Académie des Sciences Paris. Ser5. A 278 (1974).
319. T. Ruggeri, A. Strumia: "Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics." Annales Institut Henri Poincaré 34 A (1981).
320. T. Ruggeri: "Galilean invariance and entropy principle for systems of balance laws. The structure of extended thermodynamics." Continuum Mechanics and Thermodynamics 1 (1989).
321. G. Boillat, T. Ruggeri: "Moment equations ⋯" loc.cit.
322. This was decisively shown by D. Gilbarg, D. Paolucci: "The structure of shock waves in the continuum theory of fluids." Journal for Rational Mechanics and Analysis 2 (1953).
323. W. Weiss: "Die Berechnung von kontinuierlichen Stoßstrukturen in der kinetischen Gastheorie." [Calculation of continuous shock structures in the kinetic theory of gases] Habilitation thesis TU Berlin (1997).
324. See also: W. Weiss: Chapter 12 in: I. Müller, T. Ruggeri: "Rational Extended Thermodynamics" loc.cit.
325. W. Weiss: "Continuous shock structure in extended Thermodynamics." Physical Review E, Part A 52 (1995).
326. Au: "Lösung nichtlinearer Probleme in der Erweiterten Thermodynamik." [Solution of non-linear problems in extended thermodynamics"]. Dissertation TU Berlin, Shaker Verlag (2001).
327. H. Grad: "The profile of a steady plane shock wave." Communications of Pure and Applied Mathematics 5 Wiley, New York (1952).
328. I. Müller, T. Ruggeri: "Rational Extended Thermodynamics." loc.cit.
329. I. Müller, T. Ruggeri: "Stationary heat conduction in radially symmetric situations-an application of extended thermodynamics." Journal of Non-Newtonian Fluid Mechanics 119 (2004).
330. E. Barbera, I. Müller: "Inherent frame dependence of thermodynamic fields in a gas." Acta Mechanica, 184 (2006) pp. 205-216. (Pubitemid 43967417)
331. H. Struchtrup, W. Weiss: "Maximum of the local entropy production becomes minimal in stationary processes." Physical Review Letters 80 (1998).
332. E. Barbera, I. Müller, D. Reitebuch, N.R. Zhao: "Determination of boundary conditions in extended thermodynamics." Continuum Mechanics and Thermodynamics 16 (2004).
333. I. Müller, D. Reitebuch, W. Weiss: "Extended thermodynamics-consistent in order of magnitude." Continuum Mechanics and Thermodynamics 15 (2003).
334. D. Reitebuch: "Konsistent geordnete Erweiterte Thermodynamik." [Consistently ordered extended thermodynamics] Dissertation TU Berlin (2004).
335. I. Müller, T. Ruggeri: "Stationary heat conduction⋯ " loc. cit. (2004).
336. equ ~ f) with a constant relaxation time T of the order of a mean time of free flight. The BGK model is popular for a quick check and qualitative results. In the present case it permits an analytical solution, which cannot be obtained by a more realistic collision term.
337. I. Müller, T. Ruggeri: "Stationary heat conduction⋯ " loc. cit (2004).
338. I. Müller, P. Strehlow: "Kinetic temperature and thermodynamic temperature." In: Dean C. Ripple (ed.) "Temperature: Its Measurement and Control in Science and Industry." Vol. 7 American Institute of Physics (2003).
339. R. Brown: "A brief account of microscopic observations made in the months of June, July and August 1827 on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies." Edinburgh New Philosophical Journal 5 (1828) p. 358.
340. S.G. Brush: "The kind of motion we call heat." loc.cit. p. 661.
341. G. Cantoni: Reale Istituto Lombardo di Scienze e Lettere. (Milano) Rendiconti (2) 1, (1868) p. 56.
342. J.H. Poincaré: In: "Congress of Arts and Science. Universal Exhibition Saint Louis 1904." Houghton, Miffin & Co. Boston and New York (1905).
343. A. Einstein: "Die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen." Annalen der Physik (4) 17 (1905) pp. 549-560.
344. All of Einstein's early papers on the Brownian motion were later edited by R. Fürth: "Untersuchungen über die Theorie der Brownschen Bewegungen." [Investigations on the theory of the Brownian movement] Akademische Verlagsgesellschaft, Leipzig (1922). This collection has been translated into English by A.D. Cowper and is available as a Dover booklet.
345. S.G. Brush: "The kind of motion we call heat." loc. cit. p. 673.
346. P.A. Schilpp (ed.): "Albert Einstein Philosopher-Scientist". New York. "Library of Living Philosophers" (1949). The Schilpp collection contains an autobiographical note by A. Einstein from which the above quotation is taken.
347. A. Einstein: "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik." [Kinetic theory of heat equilibrium and of the second law of thermodynamics] Annalen der Physik (4) 9 (1902)pp. 417-433.
348. A. Einstein: "Investigations⋯" loc.cit. § 4.
349. Robert Andrews Millikan (1868-1953)-the man who determined the elementary charge e-writes in his autobiography: The amazing thing is that this question could be debated at all at that time [1904] ⋯ and that even the brilliant philosopher Ernst Mach could at that epoch oppose atomic theories. R. A. Millikan: "The autobiography of Robert A. Millikan." Arno Press, New York (1980). D. Lindley, the author of "Boltzmann's atom" loc.cit. writes: To an audience of young. New World scientists, this debate must have seemed an intrusion into their fresh universe. from the Old World's attic.
350. S.G. Brush: "The kind of motion we call heat." loc.cit. p. 681.
351. P. Langevin: Comptes Rendues Paris 146 (1908) p. 530.
352. According to J. Meixner: "Chemie Nobelpreis 1968 für Lars Onsager." [Nobel prize 1968 for chemistry for Lars Onsager] Physikalische Blätter 2 (1969).
353. N.A. Clarke: "Inelastic light scattering from density fluctuations in dilute gases. The kinetic-hydrodynamic transition in a monatomic gas." Physical Review A 12 (1975).
354. W. Weiss: "Zur Hierarchie der Erweiterten Thermodynamik." loc. cit.
355. See also: W. Weiss, I. Müller: "Light scattering and extended thermodynamics." Continuum Mechanics and Thermodynamics 7 (1995).
356. A lucid description of this remarkable instrument is given by G. Simonsohn: "The role of the first order auto-correlation function in conventional grating spectroscopy." Optics Communications 5 (1972).
357. See also: I. Müller, T. Ruggeri: "Rational Extended Thermodynamics." loc.cit. pp. 233-236.
358. F. Jüttner: "Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie." [Maxwell's law of the velocity distribution in the theory of relativity] Annalen der Physik 84 (1911) pp. 856-882.
359. F. Jüttner: "Die Dynamik eines bewegten Gases in der Relativtheorie." [Dynamics of a moving gas in the theory of relativity] Annalen der Physik 35 (1911) pp. 145-161. The first paper deals with a gas at rest, while the second one deals with a moving gas. The second paper is much influenced by Planck's erroneous opinion that temperature should be transformed between two Lorentz frames, see below. In my account I present a streamlined modern version.
360. A. Einstein: Sitzungsberichte (1924) loc. cit.
361. E. Fermi: Zeitschrift für Physik (1926) loc.cit.
362. P.A.M. Dirac: Proceedings of the Royal Society (1927) loc.cit.
363. F. Jüttner: "Die relativistische Quantentheorie des idealen Gases." [The relativistic quantum theory of the ideal gas] Zeitschrift für Physik 47 (1964), pp. 542-566.
364. S.R. de Groot, W.A. van Leeuven, Ch.G. van Weert: "Relativistic Kinetic Theory." North Holland Publishers Amsterdam (1980).
365. I. Müller, T. Ruggeri: "Rational Extended Thermodynamics." loc.cit. (1998).
366. C. Cercignani, G.M. Kremer: "The Relativistic Boltzmann Equation. Theory and Applications." Birkhäuser Verlag, Basel (2002).
367. S. Chandrasekhar: "The maximum mass of ideal white dwarfs." Astrophysical Journal 74 (1931) p. 81.
368. S. Chandrasekhar: "The highly collapsed configurations of a stellar mass, I and II." Monthly Notices of the Royal Astronomical Society 91 (1931) p. 456 and 95 (1935) p. 207.
369. See also: S. Chandrasekhar: "An Introduction to the Study of Stellar Structure" University of Chicago Press (1939). This book is available in a Dover edition, first published in 1957.
370. J.L Synge: "The Relativistic Gas." North Holland, Amsterdam (1957).
371. C. Eckart: "The thermodynamic of irreversible processes III: Relativistic theory of the simple fluid." loc. cit.
372. I. Müller: "Zur Ausbreitungsgeschwindigkeit⋯" Dissertation (1966) loc. cit.
373. A streamlined version of relativistic extended thermodynamics may be found in: I-Shih Liu, I. Müller, T. Ruggeri: "Relativistic thermodynamics of gases." Annals of Physics 169 (1986).
374. W. Israel: "Nonstationary irreversible thermodynamics: A causal relativistic theory." Annals of Physics 100 (1976).
375. G. Boillat, T. Ruggeri: "Moment equations in the kinetic theory of gases and wave velocities." (1997) loc.cit.
376. I. Müller: "Speeds of propagation in classical and relativistic extended thermodynamics." http:/www.livingreviews.org/Articles/Volume2/ 1999-1mueller.
377. N.A. Chernikov: "The relativistic gas in the gravitational field." Acta Physica Polonica 23 (1964).
378. N.A. Chernikov: "Equilibrium distribution of the relativistic gas." Acto Physica Polonica 26 (1964).
379. N.A. Chernikov: "Microscopic foundation of relativistic hydrodynamics." Acta Physica Polonica 27 (1964).
380. H. Minkowski: "Raum und Zeit." [Space and time] Address delivered at the 80th Assembly of German Natural Scientists and Physicists, at Cologne. September 21st, 1908. The address has been translated into English and is reprinted in "The Principle of Relativity. A collection of original memoirs on the special and general theory of relativity." Dover Publications pp. 75-91
381. See: I. Müller, T. Ruggeri: "Rational Extended Thermodynamics." loc. cit.
382. M. Planck: "Zur Dynamik bewegter Systeme." [On the dynamics of moving systems] Sitzungsberichte der königlichen preußischen Akademie der Wissenschaften (1907). Printed version: Annalen der Physik 26 (1908) p. 1.
383. A. Einstein: "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen." [On the principle of relativity and the conclusions drawn from it] Jahrbuch der Radioaktivität und Elektronik 4 (1907) pp. 411-462. Reprinted in: "Albert Einstein, die grundlegenden Arbeiten." [Albert Einstein, the basic works] K.v. Meyenn (ed) Vieweg Verlag (1990). In the reprinting the modified Gibbs equation is misprinted: It says dQ instead of dG.
384. H. Ott: "Lorentz-Transformation der Wärme und der Temperatur." [Lorentz transformation of heat and temperature] Zeitschrift für Physik 175 (1963) 70-104.
385. W. Israel, J.M. Stewart: "On transient relativistic thermodynamics and kinetic theory II." Proceeding of the Royal Society London Ser. A 365 (1979).
386. www.maths.soton.ac.uk/staff/Landsberg
387. In his later years Bohr expressed doubts that life functions can be reduced to physics and chemistry. See: N. Bohr: "Atomphysik und menschliche Erkenntnis." [Atomic physics and human knowledge] Vieweg Verlag, Braunschweig (1985).
388. E. Schrödinger: "What is life? The physical aspect of the living cell" Cambridge: At the University Press, New York: The Macmillan Company (1945) p. 75.
389. M. Rubner: "Gesetze des Energieverbrauchs bei der Ernährung." [Laws of energy consumption in nutrition] (1902).
390. I. Asimov: "Biographies⋯" loc.cit. p. 268.
391. E. Schrödinger: "What is life? The physical aspect of the living cell." Cambridge: At the University Press. New York: Macmillan Company (1945).
392. E. Schrödinger: "What is life? ⋯" loc.cit. p. 70.
393. I. Asimov: "Biographies ⋯" loc.cit. p. 621.
394. I. Asimov: "Life and Energy." Avon Publishers of Bard, New York (1972). I owe much of the information presented in this chapter to the study of that book by Asimov. On these pages I have often quoted Asimovs book of biographies and occasionally other science essays by the author. Indeed, if the truth were known, I do admire Asimov's way of writing,-except when he writes Science Fiction.
395. E. Schrödinger: "Was ist Leben? Die lebende Zelle mit den Augen des Physikers betrachtet." 2nd edition. A. Francke Verlag, Bern and Leo Lehnen Verlag, München (1951).
396. E.g. see W. Larcher: "Ökophysiologie der Pflanzen. Leben, Leistung und Stressbewältigung der Pflanzen in ihrer Umwelt" [Ecophysiology of plants. Life, performance and stress management of plants in their environment] 5. Auflage, Verlag Eugen Ulmer Stuttgart (1994).
397. As far as I know, this idea was first presented by myself and A. Klippel in the paper: A. Klippel, I. Müller: "Plant growth-a thermodynamicist's view." Continuum Mechanics and Thermodynamics 9, (1997).
398. I have suggested an alternative accompanying process,-leaving out entropic radiation altogether-, namely the mixing of the water evaporated by the leaf with the surrounding air. A. Klippel, I. Müller: "Plant growth ⋯" loc.cit.