The European Physical Journal H

, Volume 38, Issue 1, pp 57–81 | Cite as

Clarifying the link between von Neumann and thermodynamic entropies

  • Alain DevilleEmail author
  • Yannick Deville


The state of a quantum system being described by a density operator ρ, quantum statistical mechanics calls the quantity  −kTr(ρlnρ), introduced by von Neumann, its von Neumann or statistical entropy. A 1999 Shenker’s paper initiated a debate about its link with the entropy of phenomenological thermodynamics. Referring to Gibbs’s and von Neumann’s founding texts, we replace von Neumann’s 1932 contribution in its historical context, after Gibbs’s 1902 treatise and before the creation of the information entropy concept, which places boundaries into the debate. Reexamining von Neumann’s reasoning, we stress that the part of his reasoning implied in the debate mainly uses thermodynamics, not quantum mechanics, and identify two implicit postulates. We thoroughly examine Shenker’s and ensuing papers, insisting upon the presence of open thermodynamical subsystems, imposing us the use of the chemical potential concept. We briefly mention Landau’s approach to the quantum entropy. On the whole, it is shown that von Neumann’s viewpoint is right, and why Shenker’s claim that von Neumann entropy “is not the quantum-mechanical correlate of thermodynamic entropy” can’t be retained.


Entropy Pure State Density Operator Quantum Statistical Mechanic Quantum Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© EDP Sciences and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Aix-Marseille Univ, IM2NP, Campus Scientifique Saint-JérômeMarseilleFrance
  2. 2.Université de Toulouse, UPS-CNRS-OMP, Institut de Recherche en Astrophysique et Planétologie (IRAP)ToulouseFrance

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