Vanishing of first-passage times near the limit of metastability

First-passage times $T_p$ for $n$-variable metastable systems vanish as the control parameter $\mu$ approaches its spinodal value ${\mu }_{c1\mathrm{}}$, with $T_p\sim {|\mu -{\mu }_{c1\mathrm{}}|}^{{\theta }_p}$ typically. The barrier height-to-noise ratio is the small parameter. The general results for the exponent ${\theta }_p$ agree with the exactly soluble $n=1\mathrm{}$ case where ${\theta }_p=\frac{1}{2}$, and are applied to the $n=4\mathrm{}$ two-mode laser, where ${\theta }_p=2\mathrm{}$ is predicted.