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Communications in Mathematical Physics

, Volume 105, Issue 1, pp 123–131 | Cite as

Sufficient subalgebras and the relative entropy of states of a von Neumann algebra

  • Dénes Petz
Article

Abstract

A subalgebraM0 of a von Neumann algebraM is called weakly sufficient with respect to a pair (φ,ω) of states if the relative entropy of φ and ω coincides with the relative entropy of their restrictions toM0. The main result says thatM0 is weakly sufficient for (φ,ω) if and only ifM0 contains the Radon-Nikodym cocycle [Dφ,Dω] t . Other conditions are formulated in terms of generalized conditional expectations and the relative Hamiltonian.

Keywords

Entropy Neural Network Statistical Physic Complex System Nonlinear Dynamics 
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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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Dénes Petz
    • 1
  1. 1.Mathematisches Institut der Universität TübingenTübingenFederal Republic of Germany

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