  An interesting class of physical systems, including those associated with
life, demonstrates the ability to hold thermalization at bay and perpetuate
states of high free-energy compared to a local environment. In this work, we
study quantum systems with no external sources or sinks for energy, heat, work,
or entropy, that allow for high free-energy subsystems to form and persist. We
initialize systems of qubits in mixed, uncorrelated states and evolve them
subject to a conservation law. We find that four qubits make up the minimal
system for which these restricted dynamics and initial conditions allow an
increase in extractable work for a subsystem. On landscapes of eight
co-evolving qubits, interacting in randomly selected subsystems at each step,
we demonstrate that restricted connectivity and an inhomogeneous distribution
of initial temperatures both lead to landscapes with longer intervals of
increasing extractable work for individual qubits. We demonstrate the role of
correlations that develop on the landscape in enabling a positive change in
extractable work.
