It is characteristic for a continuous phase transition that the energy difference between ordered and disordered phase disappears at the transition point. This implies that fluctuations between both phases will become arbitrarily large. Not only the spatial correlation lengths diverge for those critical phenomena, but fluctuations between both phases also become arbitrarily slow in time, described by the divergence of the relaxation time. If a system is cooled at any non-zero rate (e.g. linearly) through a continuous phase transition, the time to reach the transition will eventually become shorter than the correlation time of the critical fluctuations. At this time, the fluctuations are too slow to follow the cooling rate; the system has fallen out of equilibrium and ceases to be adiabatic. A "fingerprint" of critical fluctuations is taken at this fall-out time and the longest-length scale of the domain size is frozen out. The further evolution of the system is now determined by this length scale. For very fast cooling rates, the system will fall out of equilibrium very early and far away from the transition. The domain size will be small. For very slow rates, the system will fall out of equilibrium in the vicinity of the transition when the length scale of critical fluctuations will be large, thus the domain size will be large, too. The inverse of this length scale can be used as an estimate of the density of topological defects, and it obeys a power law in the quench rate. This prediction is universal, and the power exponent is given in terms of the critical exponents of the transition.