  Evaluating the role of perturbations versus the intrinsic coherent dynamics
in driving to equilibrium is of fundamental interest to understand quantum
many-body thermalization, in the quest to build ever complex quantum devices.
Here we introduce a protocol that scales down the coupling strength in a
quantum simulator based on a solid-state nuclear spin system, leading to a
longer decay time T2, while keeping perturbations associated to control error
constant. We can monitor quantum information scrambling by measuring two
powerful metrics, out-of-time-ordered correlators (OTOCs) and Loschmidt Echoes
(LEs). While OTOCs reveal quantum information scrambling involving hundreds of
spins, the LE decay quantifies, via the time scale T3, how well the scrambled
information can be recovered through time reversal. We find that when the
interactions dominate the perturbation, the LE decay rate only depends on the
interactions themselves, T3 ~ T2, and not on the perturbation. Then, in an
unbounded many-spin system, decoherence can achieve a perturbation-independent
regime, with a rate only related to the local second moment of the Hamiltonian.
