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Consistent thermostatistics forbids negative absolute temperatures

Nature Physics volume 10, pages 67–72 (2014)Cite this article

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Abstract

Over the past 60 years, a considerable number of theories and experiments have claimed the existence of negative absolute temperature in spin systems and ultracold quantum gases. This has led to speculation that ultracold gases may be dark-energy analogues and also suggests the feasibility of heat engines with efficiencies larger than one. Here, we prove that all previous negative temperature claims and their implications are invalid as they arise from the use of an entropy definition that is inconsistent both mathematically and thermodynamically. We show that the underlying conceptual deficiencies can be overcome if one adopts a microcanonical entropy functional originally derived by Gibbs. The resulting thermodynamic framework is self-consistent and implies that absolute temperature remains positive even for systems with a bounded spectrum. In addition, we propose a minimal quantum thermometer that can be implemented with available experimental techniques.

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Figure 1: Non-negativity of the absolute temperature in quantum systems with a bounded spectrum.

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Acknowledgements

We thank I. Bloch, W. Hofstetter and U. Schneider for constructive discussions. We are grateful to M. Campisi for pointing out equation (14), and to P. Kopietz, P. Talkner, R. E. Goldstein and, in particular, P. Hänggi for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue E17-412, Cambridge, Massachusetts 02139-4307, USA

    Jörn Dunkel

  2. Max Planck Institute for Astrophysics, Karl-Schwarzschild-Straße 1, Garching 85748, Germany

    Stefan Hilbert

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  1. Jörn Dunkel
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All authors contributed to all aspects of this work.

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Correspondence to Jörn Dunkel.

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The authors declare no competing financial interests.

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Dunkel, J., Hilbert, S. Consistent thermostatistics forbids negative absolute temperatures. Nature Phys 10, 67–72 (2014). https://doi.org/10.1038/nphys2815

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