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Notes on microstate free entropy of projections

Fumio Hiai·Yoshimichi Ueda
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Abstract

We study the microstate free entropy 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 their free entropy (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 the microstate free entropy of projections.

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Fumio Hiai, Yoshimichi Ueda. 2006-05-24. Notes on microstate free entropy of projections. https://doi.org/10.2977/prims%2F1207921076

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