We present a novel path‐integral method for the determination of time‐dependent and time‐averaged reaction rates in multidimensional, periodically driven escape problems at weak thermal noise. The so obtained general expressions are evaluated explicitly for the situation of a sinusoidally driven, damped particle with inertia moving in a metastable, piecewise parabolic potential. A comparison with data from Monte‐Carlo simulations yields a very good agreement with our analytic results over a wide parameter range.
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