Notes on Microstate Free Entropy of Projections

Fumio Hiai, Yoshimichi Ueda
2008 Publications of the Research Institute for Mathematical Sciences  
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.
doi:10.2977/prims/1207921076 fatcat:lpxgzdl6wvfzlnu6ntqyzec25a