  In this article, we prove the Eyring-Kramers formula for non-reversible
metastable diffusion processes that have a Gibbs invariant measure. Our result
indicates that non-reversible processes exhibit faster metastable transitions
between neighborhoods of local minima, compared to the reversible process
considered in [Bovier, Eckhoff, Gayrard, and Klein, J. Eur. Math. Soc. 6:
399-424, 2004]. Therefore, by adding non-reversibility to the model, we can
indeed accelerate the metastable transition. Our proof is based on the
potential theoretic approach to metastability through accurate estimation of
the capacity between metastable valleys. We carry out this estimation by
developing a novel method to compute the sharp asymptotics of the capacity
without relying on variational principles such as the Dirichlet principle or
the Thomson principle.
