BOLTZMANN, Ludwig (1844-1906). Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, respective den Sätzen über das Wärmegleichgewicht. Offprint from: Sitzb. der k. Akad. der Wissensch., Band 76. Vienna, 1877. Original printed wrappers. FIRST EDITION, offprint issue. -- [With]: 11 offprints by Boltzmann, all but one from the Sitzb. der k. Akad. Wissensch. Cloth folding case.
This is the paper in which Boltzmann first described "Boltzmann's principle," the famous relation between entropy and probability, expressed in the equation S = k log W, which Boltzmann first developed in the above paper. "This equation is inscribed on Boltzmann's tombstone. S stands for the numerical value of the entropy of a given system, W for the thermodynamical (atomistic) probability of the same system, differing only by a numerical factor from the ordinary (mathematical) probability, and k is a universal constant whose numerical value has been determined and which Planck named the Boltzmann constant. . . . [According to Fritz Hasenöhrl, editor of Boltzmann's scientific papers] 'The result of this investigation, the theorem that entropy is proportional to the logarithm of the probability, is one of the most profound, most beautiful theorems of theoretical physics, indeed of all science'" (Broda, pp. 81-83). Pais writes that "the essence of [Boltzmann's principle], the insight that the second law of thermodynamics can be understood only in terms of a connection between entropy and probability, is one of the great advances of the nineteenth century" (Subtle is the Lord, p. 60).
Boltzmann's reputation as a theoretical physicist rests largely on his fundamental contributions to the kinetic theory of matter and to statistical mechanics, which laid the groundwork for Planck's development of quantum theory and for much of Einstein's work before 1925. Pais devotes an entire chapter to Einstein's use and elaboration of Boltzmann's ideas, particularly in relation to probability and the second law of thermodynamics. Early in his career Einstein (who was then unfamiliar with the work of Boltzmann and Willard Gibbs) independently developed statistical mechanics and the molecular-kinetic theory of thermodynamics, and between 1901 and 1925 he wrote close to 40 papers bearing in varying degrees on these subjects -- including his famous 1905 papers on the light-quantum hypothesis (introduced in this paper with the help of an argument based on Boltzmann statistics) and on Brownian motion.
The collection offered here also contains eleven other offprints by Boltzmann dealing with various aspects of kinetic theory, all but one published in the eight years between 1875 and 1882. A list is available on request. (12)