  A hidden-variable model is explicitly constructed by use of a Liouvillian
description for the dynamics of two coupled spin-1/2 particles. In this model,
the underlying Hamiltonian trajectories play the role of deterministic hidden
variables, whereas the shape of the initial probability distribution figures as
a hidden variable that regulates the capacity of the model in producing
correlations. We show that even though the model can very well describe the
short-time entanglement dynamics of initially separated pure states, it is
incapable of violating the Clauser-Horne-Shimony-Holt inequality. Our work
suggests that, if one takes the reluctance of a given quantum resource to be
emulated by a local-hidden-variable model as a signature of its nonclassicality
degree, then one can conclude that entanglement and nonlocality are
nonequivalent even in the context of two-qubit pure states.
