Boltzmann's H-theorem, its discontents, and the birth of statistical mechanics

A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann's H-theorem, and its simplified variant in the Ehrenfests’ 1912 wind-tree model. The little-cited 1896 (measure-theoretic) objection of Zermelo (similar to an 1889 argument due to Poincaré) is also analysed. Significant differences between the objections are highlighted, and several old and modern misconceptions concerning both them and the H-theorem are clarified. We give particular emphasis to the radical nature of Poincaré's and Zermelo's attack, and the importance of the shift in Boltzmann's thinking in response to the objections taken together.