  We investigate how entanglement spreads in time-dependent states of a 1+1
dimensional conformal field theory (CFT). The results depend qualitatively on
the value of the central charge. In rational CFTs, which have central charge
below a critical value, entanglement entropy behaves as if correlations were
carried by free quasiparticles. This leads to long-term memory effects, such as
spikes in the mutual information of widely separated regions at late times.
When the central charge is above the critical value, the quasiparticle picture
fails. Assuming no extended symmetry algebra, any theory with $c>1$ has
diminished memory effects compared to the rational models. In holographic CFTs,
with $c \gg 1$, these memory effects are eliminated altogether at strong
coupling, but reappear after the scrambling time $t \gtrsim \beta \log c$ at
weak coupling.
