  Thermally activated phenomena in physics and chemistry, such as
conformational changes in biomolecules, liquid film rupture, or ferromagnetic
field reversal, are often associated with exponentially long transition times
described by Arrhenius' law. The associated subexponential prefactor, given by
the Eyring-Kramers formula, has recently been rigorously derived for systems in
detailed balance, resulting in a sharp limiting estimate for transition times
and reaction rates. Unfortunately, this formula does not trivially apply to
systems with conserved quantities, which are ubiquitous in the sciences: The
associated zeromodes lead to divergences in the prefactor. We demonstrate how a
generalised formula can be derived, and show its applicability to a wide range
of systems, including stochastic partial differential equations from
fluctuating hydrodynamics, with applications in rupture of nanofilm coatings
and social segregation in socioeconomics.
