  Quantitative estimates for the top Lyapunov exponents for systems of
stochastic reaction-diffusion equations are proven. The treatment includes
reaction potentials with degenerate minima. The proof relies on an asymptotic
expansion of the invariant measure, with careful control on the resulting error
terms. As a consequence of these estimates, synchronisation by noise is deduced
for systems of stochastic reaction-diffusion equations for the first time.
