Notes on Microstate Free Entropy of Projections | Zendy

Fumio Hiai | Zendy; Yoshimichi Ueda | Zendy

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Notes on Microstate Free Entropy of Projections

Author(s) -

Fumio Hiai,

Yoshimichi Ueda

Publication year - 2008

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1207921076

Subject(s) - ministate , mathematics , statistical physics , entropy (arrow of time) , psychology , physics , thermodynamics , neuroscience , electroencephalography

We study the microstate free entropy χproj(p1 ,...,p n) 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.

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