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I get an impression from this enyclopedia entry

that the primary source of the Boltzmann entropy equation $S = k \log W$ might be

1866, Über die Mechanische Bedeutung des Zweiten Hauptsatzes der Wärmetheorie, Wiener Berichte, 53: 195–220; in WA I, paper 2.

I cannot read German. The only PDF I was able to obtain did not have a text-layer, so I could not copy-paste parts into Google Translate. Eventually I might go through and hand-type the whole thing into Google translate, but in the interim I would appreciate assistance expediting my search.

What is the original source of the Boltzmann entropy equation?

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    $\begingroup$ The introduction of the linked publication states "The intended purpose of this paper is to provide a purely analytical, completely generalized proof of the second law of thermodynamics, as well as identify a corresponding law of mechanics." During a quick perusal of the paper, I did not spot anything that corresponds to the entropy equation, but may have overlooked it. $\endgroup$
    – njuffa
    May 24, 2022 at 22:42
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    $\begingroup$ I don't have time to follow up right now, but the relevant publication may be: L. Boltzmann, "Über die Beziehung zwischen dem zweiten Hauptsatz der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht", Wiss. Abhandlungen, Band II, p. 163-223 (1877). In other words, it is to be found in volume 2 of his collected works. Right now I have no idea about the original publication venue. $\endgroup$
    – njuffa
    May 24, 2022 at 22:55
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    $\begingroup$ One source I consulted claims that the simple entropy formula given in the question is due to Planck and cannot be found in this form in any of Boltzmann's works. Supposedly the closest equation in a publication by Boltzmann is found on page 172 of Vorlesungen über Gastheorie: 2. Teil, 1898 (tr.: Lectures on gas theory, part 2). There we find $S = R M l \mathfrak{W}$, where $l$ denotes the natural logarithm and $M$ is the mass of a hydrogen atom. $\endgroup$
    – njuffa
    May 24, 2022 at 23:19
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    $\begingroup$ Related question: hsm.stackexchange.com/questions/6882/… $\endgroup$
    – njuffa
    May 24, 2022 at 23:28

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