Notes on microstate free entropy of projections

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.

References in corpus (3)

• Large deviations and stochastic calculus for large random matrices
• Large deviations for functions of two random projection matrices
• A log-Sobolev type inequality for free entropy of two projections

Cited by in corpus (6)

• Liberation of Projections
• Strong Convergence of Unitary Brownian Motion
• Orbital approach to microstate free entropy
• A log-Sobolev type inequality for free entropy of two projections
• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
• Remarks on free mutual information and orbital free entropy