Stronger subadditivity of entropy

Journal Article · Wed Jun 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.062329· OSTI ID:20717894

Lieb, Elliott H; Seiringer, Robert ^[1]

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1. Department of Physics, Jadwin Hall, Princeton University, P.O. Box 708, Princeton, New Jersey 08544 (United States)

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[{rho}]=-Tr({rho} ln {rho}) of a density matrix {rho}{sub 123} on the product of three Hilbert spaces satisfies S[{rho}{sub 123}]-S[{rho}{sub 12}]{<=}S[{rho}{sub 23}]-S[{rho}{sub 2}]. We strengthen this to S[{rho}{sub 123}]-S[{rho}{sub 12}]{<=}{sigma}{sub {alpha}}n{sup {alpha}}(S[{rho}{sub 23}{sup {alpha}}]-S= [{rho}{sub 2}{sup {alpha}}]), where the n{sup {alpha}} are weights and the {rho}{sub 23}{sup {alpha}} are partitions of {rho}{sub 23}. Correspondingly, there is a strengthening of the theorem that the map A map Tr exp[L+ln A] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.

• OSTI ID: 20717894
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 71; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ANNIHILATION OPERATORS
DENSITY MATRIX
EIGENSTATES
ENTROPY
GASES
HILBERT SPACE
QUANTUM FLUIDS
QUANTUM MECHANICS