  The extension $k \mapsto \mu^{\boxplus k}$ of the concept of a free
convolution power to the case of non-integer $k \geq 1$ was introduced by
Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in
random matrix theory. In this paper we give two proofs of the monotonicity of
the free entropy and free Fisher information of the (normalized) free
convolution power in this continuous setting, and also establish an intriguing
variational description of this process.
