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Negative temperatures and the definition of entropy

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  • Swendsen, Robert H.
  • Wang, Jian-Sheng

Abstract

The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Several researchers have identified the thermodynamic entropy exclusively with the “volume entropy” suggested by Gibbs, and have further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We disagree with these conclusions. We demonstrate that volume entropy is inconsistent with the postulates of thermodynamics for systems with non-monotonic energy densities, while a definition of entropy based on the probability distributions of macroscopic variables does satisfy the postulates of thermodynamics. Our results confirm that negative temperature is a valid extension of thermodynamics.

Suggested Citation

  • Swendsen, Robert H. & Wang, Jian-Sheng, 2016. "Negative temperatures and the definition of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 24-34.
    • Handle: RePEc:eee:phsmap:v:453:y:2016:i:c:p:24-34
    DOI: 10.1016/j.physa.2016.01.068
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    References listed on IDEAS

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    1. Dunkel, Jörn & Hilbert, Stefan, 2006. "Phase transitions in small systems: Microcanonical vs. canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 390-406.
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    Cited by:

    1. Matty, Michael & Lancaster, Lachlan & Griffin, William & Swendsen, Robert H., 2017. "Comparison of canonical and microcanonical definitions of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 474-489.
    2. Kalogeropoulos, Nikolaos, 2022. "Coarse-graining and symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    3. Jarzynski, Christopher, 2020. "Fluctuation relations and strong inequalities for thermally isolated systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).

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    1. Matty, Michael & Lancaster, Lachlan & Griffin, William & Swendsen, Robert H., 2017. "Comparison of canonical and microcanonical definitions of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 474-489.

    More about this item

    Keywords

    Negative temperature; Entropy;

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