Synchronisation by noise occurs when trajectories of a randomly perturbed system which evolves in time converge to each other and it has interesting applications in numerical sampling of invariant probability measures for SPDES. In the case of scalar-valued SPDEs synchronisation by noise has been investigated to a great extend based on order-preservation techniques. However, for vector-valued systems results are limited, and mostly restricted to SDEs, due to the lack of comparison principles. The standard approach for deducing synchronisation by noise for systems of S(P)DEs requires to show the negativity of the top Lyapunov exponent, a non-trivial task even in the finite-dimensional case. In this talk I will discuss a possible approach to obtain quantitative estimates on the top Lyapunov exponent via asymptotic expansions in the noise intensity, including the treatment of reaction potentials with degenerate minima. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time. Based on a joint work with Benjamin Gess.