  Time evolution of macroscopic systems is re-examined primarily through
further analysis and extension of the equation of motion for the density matrix
$\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical
probabilities it is necessary to account for changes in both in the presence of
external influences, yet standard treatments tend to neglect the former. A
model of time-dependent classical probabilities is presented to illustrate the
required type of extension to the conventional time-evolution equation, and it
is shown that such an extension is already contained in the definition of the
density matrix.
