Ehrenfest and Ehrenfest-Afanassjewa on Why Boltzmannian and Gibbsian Calculations Agree

The relation between the Boltzmannian and the Gibbsian formulations of statistical mechanics is one of the major conceptual issues in the foundations of the discipline. In their celebrated review of statistical mechanics, Paul Ehrenfest and Tatiana Ehrenfest-Afanassjewa discuss this issue and offer an argument for the conclusion that Boltzmannian equilibrium values agree with Gibbsian phase averages. In this paper, we analyse their argument, which is still important today, and point out that its scope is limited to dilute gases.