A Fundamental Property of Quantum-Mechanical Entropy

Elliott H. Lieb and Mary Beth Ruskai
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Elliott H. Lieb: Institut des Hautes Etudes Scientifiques
Mary Beth Ruskai: Massachusetts Institute of Technology, Department of Mathematics

A chapter in Inequalities, 2002, pp 59-61 from Springer

Abstract: 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.

Keywords: Density Matrix; Pure State; Generalize Entropy; Physical Review Letter; Arbitrary Region (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-3-642-55925-9_5

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