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A Fundamental Property of Quantum-Mechanical Entropy

In: Inequalities

Author

Listed:
  • Elliott H. Lieb

    (Institut des Hautes Etudes Scientifiques)

  • Mary Beth Ruskai

    (Massachusetts Institute of Technology, Department of Mathematics)

Abstract

There are some properties of entropy, such as concavity and subadditivity, that are known to hold (in classical and in quantum mechanics) irrespective of any assumptions on the detailed dynamics of a system. These properties are consequences of the definition of entropy as S(p) =—Trp lnp (quantum), (1a) S(p) =- f p lnp (classical continuous), (1b) S(p)= p i Inpi (classical discrete), (1c) where Tr means trace, p is a density matrix in (1a), and p is a distribution function (usually on R 6n) in (1b). In (1c) the p i are discrete energy level probabilities.

Suggested Citation

  • Elliott H. Lieb & Mary Beth Ruskai, 2002. "A Fundamental Property of Quantum-Mechanical Entropy," Springer Books, in: Michael Loss & Mary Beth Ruskai (ed.), Inequalities, pages 59-61, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55925-9_5
    DOI: 10.1007/978-3-642-55925-9_5
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