  We study the short-time evolution of the bipartite entanglement in quantum
lattice systems with local interactions in terms of the purity of the reduced
density matrix. A lower bound for the purity is derived in terms of the
eigenvalue spread of the interaction Hamiltonian between the partitions.
Starting from an initially separable state the purity decreases as $1 -
(t/\tau)^2$, i.e. quadratically in time, with a characteristic time scale
$\tau$ that is inversly proportional to the boundary size of the subsystem,
i.e., as an area-law. For larger times an exponential lower bound is derived
corresponding to the well-known linear-in-time bound of the entanglement
entropy. The validity of the derived lower bound is illustrated by comparison
to the exact dynamics of a 1D spin lattice system as well as a pair of coupled
spin ladders obtained from numerical simulations.
