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We prove an Eyring-Kramers law for the small eigenvalues and meanfirst-passage times of a metastable Markovian jump process which is invariantunder a group of symmetries. Our results show that the usual Eyring-Kramers lawfor asymmetric processes has to be corrected by a factor computable in terms ofstabilisers of group orbits. Furthermore, the symmetry can produce additionalArrhenius exponents and modify the spectral gap. The results are based onrepresentation theory of finite groups.

The Eyring-Kramers law for Markovian jump processes with symmetries