  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.

Operator Algebras