Entropy Inequalities

  • Huzihiro Araki
  • Elliott H. Lieb


Some inequalities and relations among entropies of reduced quantum mechanical density matrices are discussed and proved. While these are not as strong as those available for classical systems they are nonetheless powerful enough to establish the existence of the limiting mean entropy for translationally invariant states of quantum continuous systems.


Density Matrix Disjoint Union Spectral Decomposition Invariant State Selfadjoint Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Huzihiro Araki
    • 1
  • Elliott H. Lieb
    • 2
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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