  Quantum Darwinism is a paradigm to understand how classically objective
reality emerges from within a fundamentally quantum universe. Despite the
growing attention that this field of research as been enjoying, it is currently
not known what specific properties a given Hamiltonian describing a generic
quantum system must have to allow the emergence of classicality. Therefore, in
the present work, we consider a broadly applicable generic model of an
arbitrary finite-dimensional system interacting with an environment formed from
an arbitrary collection of finite-dimensional degrees of freedom via an
unspecified, potentially time-dependent Hamiltonian containing at most two-body
interaction terms. We show that such models support quantum Darwinism if the
set of operators acting on the system which enter the Hamiltonian satisfy a set
of commutation relations with a pointer observable and with one other. We
demonstrate our results by analyzing a wide range of example systems: a qutrit
interacting with a qubit environment, a qubit-qubit model with interactions
alternating in time, and a series of collision models including a minimal model
of a quantum Maxwell demon.
