2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158799We 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.15 pages, 5 figuresStatistical Mechanicstext