Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.


Not hotter than hot

A careful revision of the rudiments of statistical physics shows that negative temperatures are artefacts of Boltzmann's approximate definition of entropy. Gibbs' version, however, forbids negative absolute temperatures and is consistent with thermodynamics.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Figure 1: Gibbs versus Boltzmann.



  1. Dunkel, J. & Hilbert, S. Nature Phys. 10, 67–72 (2014).

    Article  ADS  Google Scholar 

  2. Braun, S. et al. Science 339, 52–55 (2013).

    Article  ADS  Google Scholar 

  3. Carr, L. D. Science 339, 42–43 (2013).

    Article  ADS  Google Scholar 

  4. Purcell, E. M. & Pound, R. V. Phys. Rev. 81, 279–280 (1951).

    Article  ADS  Google Scholar 

  5. Ramsey, N. M. Phys. Rev. 103, 20–28 (1956).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Igor M. Sokolov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sokolov, I. Not hotter than hot. Nature Phys 10, 7–8 (2014).

Download citation

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing