Two notions of free entropy differ even when both are finite

Constructs a bounded self-adjoint tuple in a tracial von Neumann algebra whose microstates and nonmicrostates free entropies satisfy $-\infty\lt \chi\lt \chi^*\lt \infty$. This answers Voiculescu’s finite-entropy equality question negatively: the matrix-approximation and free-Fisher-information definitions differ even when both are finite.