  We study scenarios in which the baryon asymmetry is generated from the decay
of a particle whose mass originates from the spontaneous breakdown of a
symmetry. This is realized in many models, including low-scale leptogenesis and
theories with classical scale invariance. Symmetry breaking in the early
universe proceeds through a phase transition that gives the parent particle a
time-dependent mass, which provides an additional departure from thermal
equilibrium that could modify the efficiency of baryogenesis from
out-of-equilibrium decays. We characterize the effects of various types of
phase transitions and show that an enhancement in the baryon asymmetry from
decays is possible if the phase transition is of the second order, although
such models are typically fine-tuned. We also stress the role of new
annihilation modes that deplete the parent particle abundance in models
realizing such a phase transition, reducing the efficacy of baryogenesis. A
proper treatment of baryogenesis in such models therefore requires the
inclusion of the effects we study in this paper.
