Notes on microstate free entropy of projections

Fumio Hiai, Yoshimichi Ueda

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Abstract

We study the microstate free entropy χproj (p 1,... , pn) of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of χproj (Theorem 4.1), in the proof of which a transportation cost inequality plays an important role. We also briefly discuss the free pressure in relation to χproj.

Original languageEnglish
Pages (from-to)49-89
Number of pages41
JournalPublications of the Research Institute for Mathematical Sciences
Volume44
Issue number1
DOIs
Publication statusPublished - Mar 2008

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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