  We theoretically study the non-Markovian dynamics of qubit systems coupled to
nonequilibrium environments with nonstationary and non-Markovian statistical
properties. The reduced density matrix of the single qubit system satisfies a
closed third-order differential equation with all the higher-order
environmental correlations taken into account and the reduced density matrix of
the two qubit system can be expressed as the Kraus representation in terms of
the tensor products of the single qubit Kraus operators. We derive the relation
between the entanglement and nonlocality of the two qubit system which are both
closely associated with the decoherence function. We identify the threshold
values of the decoherence function to ensure the existences of the concurrence
and nonlocal quantum correlations for a given evolution time when the two qubit
system is initially prepared in the composite Bell states and the extended
Werner states, respectively. It is shown that the environmental nonstationary
feature can suppress the decoherence and disentanglement dynamics and can
reduce the coherence and entanglement revivals in non-Markovian dynamics
regime. In addition, it is shown that the environmental non-Markovian feature
can enhance the coherence revivals in the single decoherence dynamics and the
entanglement revivals in the two qubit disentanglement dynamics, respectively.
Furthermore, the environmental nonstationary and non-Markovian features can
enhance the nonlocality of the two qubit system.
