The Question of Negative Temperatures in Thermodynamics and Statistical Mechanics

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We show that both positive and negative absolute temperatures and monotonically increasing and decreasing entropy in adiabatic processes are consistent with Carathéodory's version of the second law and we explore the modifications of the Kelvin--Planck and Clausius versions which are needed to accommodate these possibilities.We show, in part by using the equivalence of distributions and the canonical distribution, that the correct microcanonical entropy, is the surface (Boltzmann) form rather than the bulk (Gibbs) form thereby providing for the possibility of negative temperatures and we counter
the contention on the part of a number of authors that the surface entropy fails to satisfy fundamental thermodynamic
Original languageEnglish
Pages (from-to)26-63
Number of pages38
JournalStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Early online date14 May 2019
Publication statusPublished - 1 Aug 2019


  • Microcanonical entropy
  • Negative temperatures
  • The Carathéodory, Kelvin–Planck and Clausius versions of the second law


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