Climate Dynamics

, Volume 45, Issue 11–12, pp 3513–3525 | Cite as

Thermodynamic disequilibrium of the atmosphere in the context of global warming

  • Junling HuangEmail author
  • Michael B. McElroy


The atmosphere is an example of a non-equilibrium system. This study explores the relationship among temperature, energy and entropy of the atmosphere, introducing two variables that serve to quantify the thermodynamic disequilibrium of the atmosphere. The maximum work, W max , that the atmosphere can perform is defined as the work developed through a thermally reversible and adiabatic approach to thermodynamic equilibrium with global entropy conserved. The maximum entropy increase, \((\Delta S)_{max}\), is defined as the increase in global entropy achieved through a thermally irreversible transition to thermodynamic equilibrium without performing work. W max is identified as an approximately linear function of \((\Delta S)_{max}.\) Large values of W max or \((\Delta S)_{max}\) correspond to states of high thermodynamic disequilibrium. The seasonality and long-term historical variation of W max and \((\Delta S)_{max}\) are computed, indicating highest disequilibrium in July, lowest disequilibrium in January with no statistically significant trend over the past 32 years. The analysis provides a perspective on the interconnections of temperature, energy and entropy for the atmosphere and allows for a quantitative investigation of the deviation of the atmosphere from thermodynamic equilibrium.


Thermodynamic disequilibrium Energy Entropy Temperature Global warming 



The work described here was supported by the National Science Foundation, NSF-AGS-1019134. Junling Huang was also supported by the Harvard Graduate Consortium on Energy and Environment. We acknowledge helpful and constructive comments from Michael J. Aziz and Peter R. Bannon and from the reviewers.

Supplementary material

382_2015_2553_MOESM1_ESM.pdf (195 kb)
Supplementary material 1 (PDF 194 kb)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Engineering and Applied SciencesHarvard UniversityCambridgeUSA
  2. 2.John F. Kennedy School of GovernmentHarvard UniversityCambridgeUSA

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