<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" align="justify"><font face="Arial, Helvetica, sans-serif"><font size="2">Under normal circumstances, a system weakly-coupled to a thermal bath exhibits monotonic relaxation to an equilibrium state. However, at time scales shorter than the memory time of the coupling to the bath, oscillations can occur (of ensemble averages, not just individual fluctuations). In particular, we have shown that a non-demolition non-selective measurement of the state of the system (i.e., measurement of an operator commuting with the reduced system state) can disturb the equilibrium with the bath leading to subsequent short time oscillations. An apparent contradiction with Lindblad's "quantum H-Theorem" is resolved. The equivalence of a non-selective measurement to a random unitary, suggests a classical analog. [N. Erez, G. Gordon, M. Nest, and G. 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