Abstract
This paper discusses an argument by Norton (in: European Philosophy of Science—Philosophy of Science in Europe and the Viennese Heritage, Vienna Circle Institute Yearbook, vol 17, Springer, Dordrecht, pp 197–210, 2014, 2016) to the effect that reversible processes in thermodynamics have paradoxical character, due to the infinite-time limit. For Norton, one can “dispel the fog of paradox” by adopting a distinction between idealizations and approximations, which he himself puts forward. Accordingly, reversible processes ought to be regarded as approximations, rather than idealizations. Here, we critically assess his proposal. In doing so, we offer a resolution of his alleged paradox based on the original work by Tatiana Ehrenfest-Afanassjeva on the foundations of thermodynamics.
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Notes
For completeness, let us mention that, for Norton, another necessary condition is that crucial properties of the finite system be preserved in the limit. Here, we shall not be concerned with it, except for noticing that what properties ought to be regarded as crucial is mostly a pragmatic matter, depending on the purpose of the description at stake, thereby making Norton’s notion of idealization become context-dependent.
The author is grateful to Lena Zuchowski for kindly helping with the English translations of Afanassjewa’s quotations from the original text in German.
More to the point, she warns that thermodynamically reversible processes should not be related to the reversibility of the microscopic laws of motion in statistical mechanics. Cfr. Uffink (2001, pp. 218 and 317) for a similar claim, which we also endorse.
In addition, he also supposes that the values of work for all such adiabatic processes form a connected interval.
That is: in every arbitrarily close neighbourhood of a given state s in \(\Gamma _{eq}\), there are states \(s'\) that cannot be approached arbitrarily closely by any adiabatic process.
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Acknowledgements
The author is indebted to Jos Uffink, who first suggested to focus on Tatjana Afanassjewa’s work and offered inspiring insight on the matter, as well as to Lena Zuchowski for helping him translate the quotations from Afanassjewa’s original text in German. He also wishes to thank several colleagues for fruitful conversations, especially Harvey Brown, Erik Curiel, Meghan Dupree, Sam Fletcher, Wayne Myrvold, Patricia Palacios, Marina Baldissera Pacchetti, Elay Shech, Pauline van Wierst and anonymous referees. Last, but not least, special thanks go to John Norton for his constant encouragement and subtle criticism.
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Valente, G. On the paradox of reversible processes in thermodynamics. Synthese 196, 1761–1781 (2019). https://doi.org/10.1007/s11229-017-1560-3
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DOI: https://doi.org/10.1007/s11229-017-1560-3