  We show that entanglement can always arise in the interaction of an
arbitrarily large system in any mixed state with a single qubit in a pure
state. This small initial purity is enough to enforce entanglement even when
the total entropy is close to maximum. We demonstrate this feature using the
Jaynes-Cummings interaction of a two level atom in a pure state with a field in
a thermal state at an arbitrarily high temperature. We find the time and
temperature variation of a lower bound on the amount of entanglement produced
and study the classical correlations quantified by the mutual information.
