  In a quantum many-body system coupled to the environment, its steady state
can exhibit spontaneous symmetry breaking when a control parameter exceeds a
critical value. In this study, we consider spontaneous symmetry breaking in
non-steady modes of an open quantum many-body system. Assuming that the time
evolution of the density matrix of the system is described by a Markovian
master equation, the dynamics of the system is fully characterized by the
eigenmodes and spectrum of the corresponding time evolution superoperator.
Among the non-steady eigenmodes with finite lifetimes, we focus on the
eigenmodes with the highest frequency, which we call the most coherent mode.
For a dissipative spin model, it is shown that the most coherent mode exhibits
a transition from a disordered phase to a symmetry-broken ordered phase, even
if the steady state does not show singular behavior. We further argue that the
phase transition of the most coherent mode induces a qualitative change in the
decoherence dynamics of highly entangled states, i.e., the Schr\"odinger's cat
states.
