Abstract
The integral relaxation time for the difference of numbers of particles in the two potential wells (IRT-N) for double-well classical spin systems is introduced. For the uniaxial symmetry, it is given by a quadrature. Unlike the previously introduced integral relaxation time for the magnetization, the IRT-N at low temperatures describes the rate of crossing the barrier under all conditions, including the strongly biased case. In the high-barrier case, the new integral relaxation time approaches the inverse of the lowest eigenvalue of the Fokker-Planck equation Λ1. It can be more conveniently found by numerical methods than the latter.