  We derive the timescale for two initially pure subsystems to become entangled
with each other through an arbitrary Hamiltonian that couples them. The
entanglement timescale is inversely proportional to the "correlated
uncertainty" between the two subsystems, a quantity which we will define and
analyze in this paper. Our result is still applicable when one of the
subsystems started in an arbitrarily mixed state, thus it generalizes the
well-known "decoherence timescale" while coupled to a thermal state.
