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

Harvey R. Brown, Wayne Myrvold, Jos Uffink

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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.

Original languageEnglish (US)
Pages (from-to)174-191
Number of pages18
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Issue number2
StatePublished - May 2009
Externally publishedYes

Bibliographical note

Funding Information:
We are very grateful to Giovanni Valente for valuable comments on an earlier version of this paper, and to Owen Maroney for very helpful discussions. We also thank the two referees for their insights and criticisms. Two of us (H. R. B and J. U.) gratefully acknowledges the support of the Perimeter Institute for Theoretical Physics, where part of this work was undertaken. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.


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