In existographies, Jules Henri Poincare (1854-1912) (IQ:180|#180) [RGM:476|1,500+] [LPKE:12] (GME:9) (GPE:63) [CR:76] was a French mathematical physicist noted his 1900 article “On the Three-body Problem and the Equations of Dynamics”, in which the recurrence theorem was established, a theorem used by German mathematician Ernst Zermelo in 1894 to seed a debate, involving those such as German physicist Max Planck and Austrian physicist Ludwig Boltzmann, on the likeliness of mechanical derivation of the second law of thermodynamics. [1]

Overview
Poincaré's 1892 Thermodynamics textbook represents the outlines of first semester lessons for college physics students. In his 1903 book Science and Hypothesis, chapter “Energy and Thermo-dynamics”, he discusses the compatibilities of the classical dynamics, such as the Hamilton’s principle, with the emerging first and second principles of thermodynamics, Poincaré asks: [3]

“Will the two principles of Mayer and Clausius assure to it foundations solid enough to last for some time?”

In the Brussels school of thermodynamics, Poincaré’s work had an influence on Belgian thermodynamicist Théophile de Donder, between 1911 and 1914.

Irreversibility debate
See main: Irreversibility
In short, Poincaré 1900 article on the three body problem argued that three particles in a system can at various times reverse to their original starting positions. This logic, in turn, directly conflicted with German physicist Rudolf Clausius’ 1854 argument that in all real processes such a transformation would “not be reversible”, in that the forward and return forces involved would not compensate each other exactly. [4]

This tension sparked a string of follow-up articles: “Mechanism and Experience” (Poincaré, 1893), “On a Theorem of Dynamics and the Mechanical Theory of Heat” (Zermelo, 1894), “Reply to Zermelo’s Remarks on the Theory of Heat” (Boltzmann, 1896), “On the Mechanical explanation of Irreversible Processes” (Zermelo, 1896), and “On Zermelo’s Paper: ‘On the Mechanical Explanation of Irreversible Processes” (Boltzmann, 1897). [5]

Poincare is said to have concluded, according to physical economics historian Philip Mirowski, that classical thermodynamics and Hamiltonian dynamics were incompatible, because no function of coordinates and momenta could have the properties of the Boltzmann entropy function. [6]

Economics
In circa 1905, Poincare wrote the following in a letter to Leon Walras: [7]

“Can satisfaction be measured? I may say that one satisfaction is greater than another, because I prefer one to the other; but I cannot say that one is two or three times greater than another … Satisfaction then is a magnitude, but not a measureable magnitude. Now is a magnitude that is not measureable therefore not amenable to mathematical theory? By no means. Temperature, for instance (at any rate before the term ‘absolute temperature’ had acquired a signification with the rise of thermodynamics), was a non-measureable magnitude. It was arbitrarily defined and measured by the expansion of mercury. It might quite as legitimately have been defined by the expansion of any other substance and measured by any function of that expansion, provided that it was a continually increasing function. Likewise, in the present case, provided that the function continually increases along with the satisfaction which it represents.”

IQ | Mislabel

See main: Mislabeled geniuses and IQ tests
Poincare, as commonly cited among IQ and genius discussions, so poorly on the Binet IQ, to note, that he was judged an imbecile (IQ=35). [8]

Hauriou
Poincaré's 1892 Thermodynamics textbook served as a basis for French lawyer-philosopher Maurice Hauriou's 1899 human thermodynamics book Lessons on Social Movement. [2]

Education
Poincaré graduated from the École Polytechnique in circa 1876, then studied mathematics and engineering at the École des Mines, graduating with a degree in ordinary engineering in 1879, and completed his PhD in science with a dissertation “On the Properties of Functions defined by Differential Equations”, under the supervision of French mathematician Charles Hermite, at the University of Paris, finishing in circa 1879. He then lectured at Caan University for a term before becoming a professor at the University of Paris, in 1881, where he remained for the rest of his career, holding chairs in mechanics, mathematical physics, probability, celestial mechanics, and astronomy.

References
1. Poincaré, Henri. (1890). “On the Three-body Problem and the Equations of Dynamics” (“Sur le Probleme des trios corps ci les equations de dynamique”), Acta mathematica, 13: 1-270, in The Kinetic Theory of Gases (pgs. 368-81), 2003, by Stephen G. Brush and Nancy S. Hall. Imperial College Press.
2. (a) Poincaré, Henri. (1892). Thermodynamique: Leçons professées pendant le premier semester 1888-1889 (Thermodynamics: First Semester Lessons 1888-1889). Gauthier-Villars.
(b) Hauriou, Maurice. (1899). Leçons sur le Mouvement Social (Lessons on Social Movement) (thermodynamique, 23+ pgs; entropie, 19+ pgs; quote, pg. 79). Paris: Larose.
3. Poincaré, Henri. (1903). Science and Hypothesis (ch. Energy and Thermodynamics, pgs. 123-39). Dover.
4. Clausius, Rudolf. (1854). "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat", (pp. 111-135), in The Mechanical Theory of Heat, 1865, John van Voorst.
5. (a) Poincaré, Henri. (1893). “Mechanism and Experience”, Revue de Metaphysique et de Morale, 1: 534-37.
(b) Zermelo, Ernst. (1894). “On a Theorem of Dynamics and the Mechanical Theory of Heat”, Annalen der Physik.
(c) Boltzmann, Ludwig. (1896). “Reply to Zermelo’s Remarks on the Theory of Heat”, Annalen der Physik. 57: 773-84.
(d) Zermelo, Ernst. (1896). “On the Mechanical explanation of Irreversible Processes”, Annalen der Physik. 59: 793-801.
(e) Boltzmann, Ludwig. (1897). “On Zermelo’s Paper: ‘On the Mechanical Explanation of Irreversible Processes’”, 60: 392-98.
6. Mirowski, Philip. (1989). More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics (pg. 65). Cambridge University Press.
7. (a) Walras, Leon. (1909). “Economique et mecanique” (quoted at end), Bussetin de la societe vaudoise des sciences naturelles, 5th series, 45 (166): 313-27; quoted by M. Antonelli (pg. 66).
(b) Edgeworth, Francis. (1915). “Recent Contributions to Mathematical Economics” (abs) (quote, pgs. 57-58), Economic Journal, 25(97):36-63.
8. Rose, Colin and Nicholl, Malcolm J. (1998). Accelerated Learning for the 21s Century (pg. 250). Dell.