Foundations of Physics

, Volume 42, Issue 4, pp 582–593 | Cite as

Choosing a Definition of Entropy that Works

  • Robert H. SwendsenEmail author


Disagreements over the meaning of the thermodynamic entropy and how it should be defined in statistical mechanics have endured for well over a century. In an earlier paper, I showed that there were at least nine essential properties of entropy that are still under dispute among experts. In this paper, I examine the consequences of differing definitions of the thermodynamic entropy of macroscopic systems.

Two proposed definitions of entropy in classical statistical mechanics are (1) defining entropy on the basis of probability theory (first suggested by Boltzmann in 1877), and (2) the traditional textbook definition in terms of a volume in phase space (also attributed to Boltzmann). The present paper demonstrates the consequences of each of these proposed definitions of entropy and argues in favor of a definition based on probabilities.


Entropy Statistical mechanics Thermodynamics Probability Distinguishability Boltzmann 



I would like to thank Jan Tobochnik for very useful comments and suggestions. I would also like to thank Dennis Dieks for an interesting discussion. Finally, I would like to thank Erwin Frey and the members of the Arnold Sommerfeld Center for Theoretical Physics in Munich for their gracious hospitality during this work.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Physics DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.Arnold Sommerfeld Center for Theoretical PhysicsLudwig-Maximilians-UniversitätMunichGermany

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