In this paper, we describe several further developments in the application of the principle of increasing mixing character, and the related principle of decreasing mixing distance, to the time-dependent behavior of macroscopic systems. There are three main parts to this paper. In the first, some basic assumptions are discussed which are sufficient for the validity of the principle of decreasing mixing distance, and the macroscopic formulation thereof. It is shown that the principle holds, not only for a system in contact with a heat bath, but also in linear thermodynamics for open systems with time-independent boundary conditions, and with nonequilibrium steady-state, rather than equilibrium, solutions. In the second part, a new proof is given for a result previously obtained by one of us which permits the formulation of the principle in terms of observable thermodynamic properties of macroscopic systems. The new proof is more general than the old, in that one of the assumptions used before has been dropped. Finally, several simple examples are discussed, which show clearly how this principle directly yields more detailed information about the time evolution of a system than is afforded by traditional thermodynamics.