"Zur quantenmechanischen Begrundung des zweiten Hauptsatzes der Warmelehre."

In: Zeitschrift fur Physik, Vol. 72, 1931. Berlin:: Julius Springer, 1931., 1931. 8vo. 767-775 pp. Navy cloth, gilt spine. Blind-stamp of the Carnegie Institution of Washington, Mount Wilson Observatory. Fine. FIRST EDITION. "In his first scientific paper at Stockholm (1931), Klein gave, in the tradition of Gibb's statistical mechanics, an explanation of the thermodynamic irreversibility paradoxically generated by mechanically reversible systems. For this purpose he used an inequality (later known as Klein's lemma) for the statistical probability given by (truncated) the density matrix introduced by Dirac." DSB. "As a further study in the field of irreversible thermodynamics, dealt with in his thesis, Klein published in important paper in 1931 'On the Quantum Mechanical Derivation of the Second Law.'" Klein's contribution demonstrates his "universal grip on the different parts of physics, in this case on both statistical thermodynamics and quantum mechanics, especially their foundations in experimental observation, a subject which Klein penetrated deeply during his early collaboration with Bohr. . . . With a most elegant and simple mathematical argument, based on a technique developed by Gibbs in 1902, Klein had succeeded in deducing [a theorem on the development in time of the expectation value of entropy. Klein's equation] is often referred to as Klein's inequality or Klein's lemma, as an auxiliary theorem to his derivation of the second law." Fischer-Hjalmars. Fischer-Hjalmars, "Oskar Klein and the molecules," in Lindstrom, ed., Proceedings of the Symposium the Oskar Klein Centenary, pp. 77-78; DSB, XVII, p. 481; Poggendorff, VI, p. 1330. (Inventory #: S6780)