Abstract
The highway of the development of entropy is marked by many great names, for example, Clausius, Gibbs, Boltzmann, Szilard, von Neumann, Shannon, Jaynes, and several others. In this article the emphasis is put on von Neumann and on quantum mechanics. The selection of the subjects reflects the taste (and the knowledge) of the author and it must be rather restrictive. In the past 50 years entropy has broken out of thermodynamics and statistical mechanics and invaded communication theory, ergodic theory and shown up in mathematical statistics, social and life sciences. It is practically impossible to present all of its features. The favourite subjects of entropy is about macroscopic phenomena, irreversibility and incomplete knowledge. In the strictly mathematical sense entropy is related to the asymptotics of probabilities or it is a kind of asymptotic behaviour of probabilities.
Work supported by the Hungarian National Foundation for Scientific Research grant no. OTKA T 032662.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A.S. Holevo, “Quantum coding theorems”, Russian Math. Surveys, 53 (1998), 1295–1331.
E.T. Jaynes, “Information theory and statistical mechanics. IP”, Phys. Rev. 108 (1956), 171–190.
R. Jozsa, “Quantum information and its properties”, in Introduction to Quantum Computation and Information, H.-K. Lo, S. Popescu and T. Spiller (eds.), World Scientific, 1998.
E.H. Lieb, M.B. Ruskai, “Proof of the strong subadditivity of quantum mechanical entropy”, J. Math. Phys. 14 (1973), 1938–1941.
J. von Neumann, “Thermodynamik quantummechanischer Gesamheiten”, Gött. Nach. 1 (1927), 273–291.
J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932.
M. Ohya, D. Petz, Quantum Entropy and its Use, Springer, 1993.
A. Peres, Quantum Theory: Concepts and Methods, Kluwer, 1993.
D. Petz, “Properties of quantum entropy”, in Quantum Probability and Related Topics VII, 275–297, World Sci. Publishing, 1992.
D. Ruelle,Statistical mechanics. Rigorous results, Benjamin, New York-Amsterdam, 1969.
G.L. Sewell, Quantum theory of collective phenomena, Clarendon Press, New York, 1986.
M. Tribus, E.C. Mclrvine, “Energy and information”, Scientific American 224 (September 1971), 178–184.
A. Wehrl, “General properties of entropy”, Rev. Mod. Phys. 50 (1978), 221–260.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Petz, D. (2001). Entropy, von Neumann and the von Neumann Entropy. In: Rédei, M., Stöltzner, M. (eds) John von Neumann and the Foundations of Quantum Physics. Vienna Circle Institute Yearbook [2000], vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2012-0_7
Download citation
DOI: https://doi.org/10.1007/978-94-017-2012-0_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5651-1
Online ISBN: 978-94-017-2012-0
eBook Packages: Springer Book Archive