  We investigate the non-equilibrium states of an interacting multi-component
quantum system when only an extensive subsystem is quantum-quenched or driven
from the ground state. As a concrete example, we consider a system where two
XXZ spin chains are coupled to a transverse field Ising (TFI) chain, and only
the transverse field in the TFI chain is quantum-quenched or periodically
driven in time, starting from an initially ordered state. This system is
studied using density matrix renormalization group (DMRG) simulations and
various entanglement entropy diagnostics. In the case of quantum quenching,
when the transverse field is suddenly switched on to become the largest energy
scale, the resulting internal dynamics leads to a pre-thermal steady state with
persistent oscillating magnetization (`self-driving') and emergent conservation
laws. Upon applying the time-dependent drive to the TFI chain (`external
driving'), sufficiently fast drive gives rise to a pre-thermal steady state
with finite magnetization, whereas a slow drive generates a high-temperature
disordered state. We briefly discuss the experimental implementation of our
protocol in organic materials with quantum-tunneling hydrogen atoms.
