= Phase slip
{title2=$\Delta\theta=\pm2\pi$}
A <phase slip> changes the continuously tracked relative <phase> by one cycle, usually $\pm2\pi$, compared with a locked state. Tracking the angle only <modulo> $2\pi$ hides this accumulated winding: the wrapped phase can return to the same value after a full circuit. A jump caused solely by changing the plotting branch cut is not evidence of a dynamical phase slip.
In a noisy locked oscillator, fluctuations usually remain close to a stable phase, but a <thermally activated phase slip> crosses a barrier of the <tilted washboard potential> and settles in a neighboring well on the real-valued phase lift. The corresponding wrapped state can look unchanged even though the relative cycle count has increased or decreased by one.
If forward and backward slips have rare-event rates $r_+$ and $r_-$, their mean contribution to unwrapped phase drift is $2\pi(r_+-r_-)$. This follows by multiplying the signed change per event by the expected event count per unit time. Equal rates can therefore give zero mean drift while individual slips still occur. The <forward-backward bias of phase slips> determines when a frequency mismatch makes one direction more likely.
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