It is believed that an isolated and far-from-equilibrium quantum many-body system will approach equilibrium via a mechanism whereby any given subsystem acts as an open quantum system that is coupled to an environment—the complementary part of the full system—and undergoes a complicated equilibration process such that all the subsystems in the long-time limit attain equilibrium states compatible with the global equilibrium state. This picture prompts the question whether the dynamics of any given subsystem is Markovian (monotonic loss of information and memory) or non-Markovian. In this work, by numerically probing the dynamical behavior of the quantum distances between temporally separated states of small subsystems, we reveal the telltale signatures of (non-)Markovianity of the dynamics of subsystems of an isolated quantum spin system brought into the far-from-equilibrium regime, exemplified with the mixed-field Ising spin chain quenched between parameter regimes deep inside its magnetically ordered and disordered regimes. Additionally, remarkably systematic behavior is seen in a measure of classical distances between the quantum states of the considered subsystems. These features strongly depend on the direction of quenching in the parameter space, with paramagnetic-to-ferromagnetic quenches offering considerably stronger signatures of subsystem non-Markovianity, for which we offer heuristic arguments.

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• Nonequilibrium statistical mechanics
• Quantum information theory
• Quantum memories
• Nonequilibrium systems
• Quantum spin models
• Markovian processes
• Non-Markovian processes
• Tensor network methods