Stronger subadditivity of entropy

Elliott H. Lieb; Robert Seiringer

doi:10.1103/PhysRevA.71.062329

Stronger subadditivity of entropy

Elliott H. Lieb, Robert Seiringer

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.

Original language	English (US)
Article number	062329
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	71
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevA.71.062329
State	Published - Jun 2005

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics

Access to Document

10.1103/PhysRevA.71.062329

Cite this

@article{20bef6173b74445294ea53252b959d3f,

title = "Stronger subadditivity of entropy",

abstract = "The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr({\"I}±ln{\"I}±) of a density matrix {\"I}±123 on the product of three Hilbert spaces satisfies S[{\"I}±123]- S[{\"I}±12]≤S[{\"I}±23]-S[{\"I}±2]. We strengthen this to S[{\"I}±123]-S[{\"I}±12] ≤αnα(S[{\"I}±23α]-S[{\"I}±2α]), where the nα are weights and the {\"I}±23α are partitions of {\"I}±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.",

author = "Lieb, {Elliott H.} and Robert Seiringer",

year = "2005",

month = jun,

doi = "10.1103/PhysRevA.71.062329",

language = "English (US)",

volume = "71",

journal = "Physical Review A - Atomic, Molecular, and Optical Physics",

issn = "1050-2947",

publisher = "American Physical Society",

number = "6",

}

TY - JOUR

T1 - Stronger subadditivity of entropy

AU - Lieb, Elliott H.

AU - Seiringer, Robert

PY - 2005/6

Y1 - 2005/6

N2 - The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.

AB - The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[±]=- Tr(Ï±lnÏ±) of a density matrix Ï±123 on the product of three Hilbert spaces satisfies S[Ï±123]- S[Ï±12]≤S[Ï±23]-S[Ï±2]. We strengthen this to S[Ï±123]-S[Ï±12] ≤αnα(S[Ï±23α]-S[Ï±2α]), where the nα are weights and the Ï±23α are partitions of Ï±23. Correspondingly, there is a strengthening of the theorem that the map A|Trexp[L+lnA] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.

UR - http://www.scopus.com/inward/record.url?scp=26944431524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26944431524&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.71.062329

DO - 10.1103/PhysRevA.71.062329

M3 - Article

AN - SCOPUS:26944431524

SN - 1050-2947

VL - 71

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 6

M1 - 062329

ER -

Stronger subadditivity of entropy

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this