A note on the attainability of states by equalizing processes

In this paper, we consider regions of attainability in certain state spaces as a function of the initial state under a well-defined and physically relevant class of processes. These processes are the continuous and chaos-enhancing processes (in the sense of Ruch and Uhlmann). It turns out that these sets have complicated geometrical structures: They are polyhedra which are generally non-convex. The proof — a rather geometrical one — is given. A theorem of Hardy, Littlewood, and Polya and properties of bistochastic matrices are used crucially.