J. W. Gibbs. Elementary Principles in Statistical Mechanics. Translated from the English by K. V. Nikolsky. State Publishing House for Technical-Theoretical Literature, Moscow–Leningrad, 1946. Price 8 rubles.

Gibbs’s book belongs to the very few works of theoretical physics of the classical period that have retained enduring significance down to our own day. Its historical fate is to some extent similar to that of its author’s thermodynamic studies. Just as the memoir “On the Equilibrium of Heterogeneous Substances” (still awaiting translation into Russian), published in 1878 and which for many decades anticipated the development of the principal branches of physical chemistry, remained outside the field of view of European scholars until the appearance in 1891 of Ostwald’s German translation [Van ’t Hoff, in his famous work Studies in Chemical Dynamics (1885), nowhere mentions Gibbs], so too the Principles of Statistical Mechanics did not immediately, after its appearance, take the place in the physical literature that properly belonged to it.

In his review of the first edition, published in 1902, of the Elementary Principles of Statistical Mechanics, M. Abraham (Physikalische Zeitschrift, vol. 3, p. 582, 1902), noting that “the exposition is very abstract,” and giving a chapter-by-chapter survey of the contents, confined himself to the general conclusion that “the essential result of the work should undoubtedly be seen in the mechanical justification of the propositions of thermodynamics relating to thermal equilibrium and to reversible processes.”

It is not, of course, surprising that Abraham, whose own scientific interests were rather far removed from statistical mechanics, passed over in silence the richest conceptual and fundamental side of Gibbs’s immortal work. Moreover, the historical circumstances of the beginning of our century could not favor a proper evaluation and wide dissemination—

in comparison with a book devoted to a branch of theoretical physics that until then had no definite experimental foundation. Let us recall that as early as 1905 A. Einstein, in his famous paper on the theory of Brownian motion, “On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular-Kinetic Theory of Heat” (Annalen der Physik, vol. 17, p. 549, 1905; cited from the Russian translation in the collection: A. Einstein and M. Smoluchowski, Brownian Motion, ONTI, 1936, p. 13), wrote: “If the motion discussed here can really be observed, together with the regularities to be expected, then an exact determination of the true atomic dimensions becomes possible. If, on the other hand, the prediction of this motion is not fulfilled, this will be a weighty argument against the molecular-kinetic conception of heat,” and concluded this article with the following appeal to experimentalists: “If any investigator should succeed in quickly resolving the questions raised here, questions important for the theory of heat!” (ibid., p. 27). As is well known, these questions were indeed very soon brilliantly resolved by the remarkable experiments of Jean Perrin, Svedberg, Il’in, and others.

It is therefore not surprising that Einstein, as follows from his later statement, did not know of Gibbs’s work when, in 1904, he published his paper “On the General Molecular Theory of Heat,” containing a method based on considering a system in a thermostat and coinciding with Gibbs’s method of the canonical ensemble (Annalen der Physik, vol. 14, p. 354, 1904).

The popularization of the Elementary Principles of Statistical Mechanics was greatly aided by the appearance in 1905 of the German translation, made by Zermelo, and by P. S. Ehrenfest’s review of this translation (Physikalische Zeitschrift, vol. 7, p. 338, 1906).

From that time down to our own day, works have appeared devoted to the further development and to various applications of Gibbs’s ideas. Let us mention here only the article by P. S. Ehrenfest and T. A. Ehrenfest-Afanassjewa in the Mathematical Encyclopedia, the Leiden dissertations of Leo Sigismundovich Ornstein (1908) and Uhlenbeck (1927), Kramers’s work devoted to Gibbs’s grand ensemble (1938), and, finally, A. Ya. Khinchin’s book Mathematical Foundations of Statistical Mechanics (1943).

One should welcome the appearance of the translation into Russian of Gibbs’s classic work, which will be studied by yet another generation of young Soviet theorists and will serve for them as a source of new ideas and original investigations.

V. K. Nikol’skii has brilliantly coped with the very difficult task of translating Gibbs’s book and, having successfully overcome the considerable difficulties connected with the author’s peculiar stylistic manner, has achieved an adequate rendering of the original.

B. N. Finkelstein