Free probability, introduced by Dan Voiculescu in 1980s, is a non-commutative parallel of classical probability theory, in which random variables are operators on a Hilbert space, and the notion of independence comes from free products. This theory has many surprising parallels with classical probability theory. It is also connected to asymptotics of random matrices as well as roots of random polynomials. In this joint work with T. Tao, we consider the concept of continuous free convolution powers that was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory. We discuss 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.