  Nuclear reactions present an interesting case for studies of the
time-evolution of entanglement between complex quantum systems. In this work,
the time-dependent nuclear density functional theory is employed to explore
entanglement in multinucleon transfer reactions. As an illustrative example,
for the reaction $^{40}$Ca $+$ $^{208}$Pb at $E_{\rm lab} = 249$ MeV, in the
interval of impact parameters $4.65-7.40$ fm, and the relativistic density
functional PC-PK1, we compute the von Neumann entropies, entanglement between
fragments, nucleon-number fluctuations, and Shannon entropy for the
nucleon-number observable. A simple linear correlation is established between
the entanglement and nucleon-number fluctuation of the final fragments. The
entanglement between the fragments can be related to the corresponding
excitation energies and angular momenta. The relationship between the von
Neumann entropy and the Shannon entropy for the nucleon-number observable is
analyzed, as well as the time-evolution of the entanglement (nucleon-number
fluctuation). The entanglement is also calculated for a range of incident
energies and it is shown how, depending on the impact parameter, the
entanglement increases with the collision energy.
