In the book "Ludwig Boltzmann, the man who trusted atoms"by C.Cercignani, I read about the thesis according to which it was Boltzmann, not Gibbs who first introduced the concept of "statistical ensemble", which however he named in a different way ("monodes"). The passage in question is the following:

"As a matter of fact a statistical ensemble (in Gibbs's terminology) is called a monode by Boltzmann. The question posed in the above-mentioned paper [ 1] is the following: what statistical families of steady distributions have the property that, when an infinitesimal change is made in their parameters, the infinitesimal changes in the average total energy of the system E, of the pressure p, and of the volume V are such that (dE + p dV)/ T (where T is the average kinetic energy per particle) is an exact differential (at least in the thermodynamic limit. when V $\rightarrow \infty$ ,N $\rightarrow \infty$ , whereas N / V remains bounded)? These families are called orthodes by Boltzmann. The answer given by Boltzmann to his own question is that there are at least two ensembles of this kind, the ergode (Gibbs's microcanonical ensemble) and the holode (Gibbs's canonica/ ensemble)."

Are there historical studies about the Boltzmann contribution to this area of research?

  • 1
    $\begingroup$ This thesis is more or less the consensus among historians now. Uffink's article in SEP surveys Boltzmann's work on ensembles and cites book length treatments. $\endgroup$
    – Conifold
    Feb 8, 2021 at 0:01


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