  We study the temporal approach to equilibrium of the Gibbs' and conditional
entropies for both invertible deterministic dynamics as well as non-invertible
stochastic systems in the presence of white noise. The conditional entropy will
either remain constant or monotonically increase to its maximum of zero.
However, the Gibbs' entropy may have a variety of patterns of approach to its
final value ranging from a monotone increase or decrease to an oscillatory
approach. We have illustrated all of these behaviors using examples in which
both entropy dynamics can be determined analytically.
