4
Entropy and Probability
4a. Einstein's Contributions at a Glance
Einstein's activities related to thermodynamics, statistical mechanics, and kinetic
theory begin with his very first paper, completed at the end of 1900, and span a
quarter of a century, during which time he wrote close to forty articles bearing in
varying degree on these subjects. The first of the vintage years was 1905, when he
developed theoretically three independent methods for finding Avogadro's number.
In an autobiographical sketch published in 1949, Einstein's comments on his
contributions to statistical physics are relatively brief. The main message is con-
tained in the following phrases: 'Unacquainted with the investigations of Boltz-
mann and Gibbs which had appeared earlier and which in fact had dealt exhaus-
tively with the subject, I developed statistical mechanics and the molecular-kinetic
theory of thermodynamics based on it. My main purpose for doing this was to
find facts which would attest to the existence of atoms of definite size' [El]. Here
he is referring to his three papers published* in the period 1902-4, in which he
made 'a rediscovery of all essential elements of statistical mechanics' [Bl]. At that
time, his knowledge of the writings of Ludwig Boltzmann was fragmentary and
he was not at all aware of the treatise by Josiah Willard Gibbs [Gl]. In 1910,
Einstein wrote that had he known of Gibbs's book, he would not have published
his own papers on the foundations of statistical mechanics except for a few com-
ments [E2]. The influential review on the conceptual basis of statistical mechanics
completed in that same year by his friends and admirers Paul Ehrenfest and
Tatiana Ehrenfest-Affanasjewa refers to these Einstein articles only in passing,
in an appendix [E3]. It is true that Einstein's papers of 1902-4 did not add much
that was new to the statistical foundations of the second law of thermodynamics.
It is also true that, as Einstein himself pointed out [E4], these papers are no pre-
requisite for the understanding of his work of 1905 on the reality of molecules.
Nevertheless, this early work was of great importance for his own further scientific
development. In particular, it contains the germ of the theory of fluctuations which
he was to apply with unmatched skill from 1905 until 1925.
It would be entirely beside the mark, however, to consider Einstein's main con-
*In 1901, he had sent the first of these papers to Zurich in the hope that it might be accepted as his
doctoral thesis; see Chapter 3.
55