This book is a faithful English translation (with a Foreword by M. Kac and G. E. Uhlenbeck and a Preface by Tatiana Ehrenfest) of a well-known article by the late Paul Ehrenfest and his wife Tatiana Ehrenfest-Afanassjewa, which was originally published in 1912 in the German “Encyklopädie der mathematischen Wissenschaften” [IV 2 II, Heft 6, 90 S. (1912; JFM 43.0763.01)]. This work is undoubtedly one of the most brilliant and fundamental which have ever been written on the subject and, as rightly stated by Kac and Uhlenbeck, “in spite of the passage of time it has lost little of its scientific and didactic value”. The few statements that the further development of physics (in particular the rising of quantum mechanics) has proved erroneous – as for instance the calling in question of the adequacy of the ergodic approach, which was suggested by the limited validity of the energy equipartition theorem – can be easily isolated from the context with no harm to the clearness of the main line of thought. The method of exposition is essentially the historical one, leaving aside however any superfluous detail.
After a discussion of the kinetic theory of matter, and especially of the Boltzmann H-theorem, the authors investigate the Gibbs and Boltzmann approaches to general statistical mechanics, comparing them step by step. The decisive superiority of the Boltzmann realistic standpoint with respect to the “platonistic” attitude of Gibbs emerges from this comparison in an evident way.
In conclusion, I consider very commendable the Cornell University Press’ decision of publishing the present translation, by means of which such an important work is made more accessible to the English speaking world (which has been perhaps too exclusively influenced by the Gibbsian tradition).