Phase slip ($\Delta \theta =\pm 2\pi$)

An event changing the unwrapped relative phase by one cycle, usually $2\pi$, compared with a phase-locked state. Thermally activated phase slips correspond to crossing neighboring barriers of a tilted washboard potential. Successive slips can produce long-term drift even while small fluctuations appear confined on shorter times.

A noise-driven barrier crossing between adjacent phase-locked wells. The Kramers escape rate is proportional to $e^{-\Delta V/T_{\mathrm{eff}}}$ when a mobility-one Langevin equation has white-noise covariance $2T_{\mathrm{eff}}\delta (t-t^{\prime })$. Both the barrier and local relaxation time determine whether an intrawell phase autocorrelation approximation is appropriate.

In a mobility-one noisy Adler phase equation, matching Kramers escape rate prefactors and a barrier difference $2\pi \omega$ give $p_{+}/p_{-}=e^{2\pi \omega /T_{\mathrm{eff}}}$. Positive mismatch favors forward winding. The ratio is a low-noise barrier-crossing result, not a claim that the particle remains in one well at arbitrarily long times.