  Revivals of quantum correlations have often been explained in terms of
back-action on quantum systems by their quantum environment(s). Here we
consider a system of two independently evolving qubits, each locally
interacting with a classical random external field. The environments of the
qubits are also independent, and there is no back-action on the qubits.
Nevertheless, entanglement, quantum discord and classical correlations between
the two qubits may revive in this model. We explain the revivals in terms of
correlations in a classical-quantum state of the environments and the qubits.
Although classical states cannot store entanglement on their own, they can play
a role in storing and reviving entanglement. It is important to know how the
absence of back-action, or modelling an environment as classical, affects the
kind of system time evolutions one is able to describe. We find a class of
global time evolutions where back-action is absent and for which there is no
loss of generality in modelling the environment as classical. Finally, we show
that the revivals can be connected with the increase of a parameter used to
quantify non-Markovianity of the single-qubit dynamics.
