The new integral relaxation time for thermal activation of spins

The integral relaxation time for the difference of populations of the two potential wells 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 former 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. It can be more conveniently found by numerical methods than the latter.