Notes on Microstate Free Entropy of Projections

  • Fumio Hiai

    Abiko, Japan
  • Yoshimichi Ueda

    Kyushu 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. 49–89

DOI 10.2977/PRIMS/1207921076