Notes on Microstate Free Entropy of Projections
Fumio HiaiAbiko, Japan
Yoshimichi UedaKyushu University, Fukuoka, Japan
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.
Cite this article
Fumio Hiai, Yoshimichi Ueda, Notes on Microstate Free Entropy of Projections. Publ. Res. Inst. Math. Sci. 44 (2008), no. 1, pp. 49–89DOI 10.2977/PRIMS/1207921076