Maximum entropy principle and Landau free energy inequality

In this paper, the following problem is considered: given two Hermitian matrices H and K and two real numbers x and y, determine a positive semidefinite matrix ρ such that the von Neumann entropy is maximum, subject to the condition that and . This question arises in information theory and in statis...

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Published inLinear & multilinear algebra Vol. 69; no. 6; pp. 1020 - 1034
Main Authors Bebiano, N., da Providência, J.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 26.04.2021
Taylor & Francis Ltd
Subjects
Entropy
Entropy (Information theory)
Free energy
Information theory
Landau free energy inequality
Mathematical analysis
Matrix methods
Maximum entropy
Maximum-entropy principle
Numerical methods
numerical range
Real numbers
Statistical inference
Statistical mechanics
Von Neumann entropy
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ISSN0308-1087
1563-5139
DOI10.1080/03081087.2019.1620163

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Summary:In this paper, the following problem is considered: given two Hermitian matrices H and K and two real numbers x and y, determine a positive semidefinite matrix ρ such that the von Neumann entropy is maximum, subject to the condition that and . This question arises in information theory and in statistical mechanics in connection with the maximum-entropy inference principle. To answer it, we use this principle and numerical range methods.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2019.1620163